Aharon, if you are a deist then that is a good basis for theism and revelation at Mount Sinai.
See the Rabbi's notebook at length here:

https://mikyab.net/Writings/Notebooks on Matters of Faith/Notebook-5-From Deism to Theism/

Thank you very much, honored Rabbi!

A. Are utensils in which food was cooked on the Sabbath forbidden until they are purged?

B. Are utensils that absorbed forbidden water, for example if water was heated in them on the Sabbath, also in need of purging, or is there not enough substance in water to impart taste?

C. Is an act that renders utensils forbidden, and causes members of the household and guests to sin unintentionally by using forbidden utensils, prohibited only for religious reasons or also for moral reasons?

A. There is a dispute about this (see section 318, subsection 1, in the Mishnah Berurah), and in any case this is only a rabbinic penalty, since regarding the food there is no intrinsic object-based prohibition (after all, after the Sabbath it is permitted to be eaten in certain circumstances and by certain people). There is room to be lenient. And if you are troubled only by the prohibition caused to others, there is even more room to be lenient, since you are causing them to stumble unintentionally in a doubtful rabbinic prohibition. This is assuming they are acting unintentionally and do not know that you cooked in the utensils. And in general, even if they are violating a prohibition, it is unintentional and under compulsion, so if your concern about "do not place a stumbling block" does not trouble you from the standpoint of your own prohibition, I do not see why to worry about their prohibition. At least with a rabbinic prohibition (and certainly with a doubt), what they do not know will not harm them. See further here:
https://mikyab.net/%D7%9B%D7%AA%D7%91%D7%99%D7%9D/%D7%9E%D7%90%D7%9E%D7%A8%D7%99%D7%9D/%D7%94%D7%A0%D7%96%D7%A7-%D7%91%D7%90%D7%9B%D7%99%D7%9C%D7%AA-%D7%97%D7%95%D7%9E%D7%A6%D7%AA-%D7%9C%D7%99%D7%9E%D7%95%D7%9F-%D7%91%D7%A4%D7%A1%D7%97-%D7%91%D7%9C%D7%99-%D7%99%D7%93%D7%99%D7%A2%D7%94/
B. That is a very nice argument. Still, one could reject it by saying that precisely because the prohibition here is due to a penalty and not an intrinsic object-based prohibition, it would not depend on taste. But practically speaking, it seems reasonable not to be stricter here than with utensils that absorbed an actual prohibition (such as a utensil that absorbed water libated for idolatry).
C. As stated above, from a religious standpoint this is mainly about you, not them. But morally there is room to discuss it. Apparently this depends on whether you are a pluralist or merely tolerant (see here the discussion in the Ritva from the passage in tractate Sukkah 10): https://mikyab.net/%D7%9B%D7%AA%D7%91%D7%99%D7%9D/%D7%9E%D7%90%D7%9E%D7%A8%D7%99%D7%9D/%D7%94%D7%90%D7%9D-%D7%94%D7%94%D7%9C%D7%9B%D7%94-%D7%94%D7%99%D7%90-%D7%A4%D7%9C%D7%95%D7%A8%D7%9C%D7%99%D7%A1%D7%98%D7%99%D7%AA/). But this too could be rejected, because if you are not certain of your position, then even if you are a pluralist, there would still be a prohibition here, since if they are right then there is a problem.

There is a mistake in the last line of the answer, right? It should say: "even if you are not a pluralist there would still be a prohibition here"?
For the pluralist has more reason to be careful not to cause someone who disagrees with him to stumble than the tolerant monist does.

To Yosef: by now it is already too late.
At the time I had bitter arguments with senior people from Arachim. The arguments (which were forced on me) revolved around the truth of certain facts which, in Rabbi Michi's opinion, are not at the core of faith and can be given up.
I asked to involve Rabbi Michi in the argument, but they absolutely refused, on the grounds that he is "worse than a Reform rabbi," because he is not willing to guarantee the fact that the entire Torah, with every letter exactly as we have it, was given and dictated to Moses at Sinai.

Indeed.
So their criterion is that whoever believes in more letters of the Torah is worse. Interesting… According to that, they are the worst, because they believe everything was given at Sinai. Into their assembly let my honor not enter—what heretics they are.

Aharon, I didn't understand you.
If Michi says things that make sense,
why does the opinion of the senior people at Arachim matter?

To Moishbb

Of course it doesn't matter what the senior people at Arachim say.
I already got stuck at the fourth notebook, which is built on theological claims, since I did not accept the axioms, and this is not the place to elaborate.
The issue is this:
In order to form a clear personal position, you need to come from a clean place, as objective as possible.
But after you go through arguments like these, which are forced on you, which include threats, manipulations ("you don't believe because of lusts / emotional problems"), and sometimes cost you money (because it is basically "treatment"), you lose trust in the religious position. And worst of all, because of the revulsion from the other side, you lose confidence in yourself that you can approach the matter with objective judgment.
And that is very sad.
As I said, the Rabbi was my lifeline; I believed that at the decisive moment he would be able to sort things out, but they absolutely refused, and then I escaped from them by the skin of my teeth.
At the moment I am sick of dealing with these matters; maybe someday time will heal what I went through, and I will feel that I can form a genuine and objective position.

By the way, by "threats" I mean warnings that if I did not "become convinced," they would make sure to break up my family and rescue my wife and children from me, so they would not be corrupted by me, God forbid.

Sad.
My heart is with you.
I wish you that you find peace in the place where you are.

With God's help, 5 Tishrei 5777

To Aharon—greetings,

I am not a halakhic decisor, but in my humble opinion there is reason to maintain that you can fulfill your wife's and your children's obligation in kiddush as one of the Jewish men,

For as appears from your words, you definitely believe in the existence of God who created the world, and regarding the other foundations of faith you are in a state of uncertainty, and at the moment you are not sure of your ability to reach an objective conclusion one way or the other, especially after the trauma you went through in the discussions with the Arachim lecturers. And since one may rely on the words of Rabbi Kook (in Letter 20) that one who is undecided is not, God forbid, a "heretic"—in my humble opinion, there is importance in the father of the family reciting kiddush for the sake of a calm family atmosphere. Especially if afterward you eat an olive-sized amount of "calm-yourself" 🙂 so that there will be kiddush in the place of a meal.

In my humble opinion there is no need to share your family with your questions of faith. Do your wife, your father-in-law, and your mother-in-law have the tools to cope with the questions you are raising? Bringing your doubts and hesitations to them will only add to their distress, which could, God forbid, also affect the marriage.

As for clarifying the questions you have about faith and answering them, extensive literature in Jewish thought has been devoted to this throughout the generations. It is a major discipline within Torah, and one needs years to go through what has been written and said about it. Great and worthy figures sat over this "crucible"—Saadia Gaon and Maimonides, Judah Halevi and Ramchal, Rabbi Kook and Rabbi Joseph Dov Soloveitchik. And in our own generation as well, there is no shortage of Torah scholars who can listen to your doubts patiently, openly, and discreetly, and perhaps give you an answer that will make sense to you.

Recently the Yedaya Institute was established, in which a number of Torah scholars and scientists joined together, people with extensive knowledge in Jewish thought and general philosophy, including Rabbi Dr. Michael Abraham, Rabbi Uri Sherki, Rabbi Dr. Moshe Rat (author of the book Simply to Believe), from whose words, books, and online lectures various issues in Jewish thought can be explained to you, and with time you will find the path suitable for you.

With blessings, S. Z. Levinger

To S. Z. L.,

I do not know why you concluded from my words that I am "undecided." I am confident in my deistic position, which I formed after much thought.
Of course my confidence is not absolutely absolute. In every position and every issue I have formed in my life, I am not one hundred percent certain. One can always be mistaken or miss something.
If I were in fact "undecided," I would keep the Sabbath.
I only noted that the trauma I underwent with Arachim prevents me from returning to the materials and discussing them again from additional viewpoints and with broader knowledge. I feel too emotionally loaded.
I do not share others with my hesitations; here on this site it just slipped out, although I do not know if this is the place. So thank you for your advice; I will only say to you that the decision "not to share" can also have serious consequences.

As for the matter itself, I will quote from Rabbi Kook's words that you cited:

And regarding the law, know that although it is a complete prohibition and a grave sickness even for one who doubts and entertains thoughts against the words of perfect faith, nevertheless we do not find that the Sages judged someone with the status of a heretic except one who denies—that is, one who decisively concludes the opposite.
And such a decisive conclusion of the opposite cannot be found in Israel in any person unless he is utterly wicked and deliberately lying, for even the greatest wickedness can do no more than cast the blemish of doubt upon the weak-minded.

And I will quote further from Halikhot Shlomo by Rabbi Shlomo Zalman Auerbach, Laws of Prayer, chapter 4, Section 15:
Rabbi Elchanan Wasserman wrote in Kovetz Shiurim (part 2, sec. 77, para. 14) that if a heretic performs a commandment it is nothing at all, since it is merely a mechanical act… (and Rabbi Shlomo Zalman disagrees): It is not mentioned anywhere that someone who is doubtful in his faith must put on tefillin again, for anyone who performs the commandment with clear awareness, even though he is doubtful in his faith, is not considered merely mechanically engaged…
If someone is in a place where it seems clear to him that now is not the first night of Passover, but he is in an environment where everyone says it is the night of Passover, and out of embarrassment he eats with them an olive-sized amount of matzah, it stands to reason that at least in his heart he intends that if the truth is as they say, he will thereby fulfill his obligation. And the same applies to an apostate and a heretic—there is some doubt in his heart. Therefore when he does something from the Torah, it is as though he intends: if the Holy One, blessed be He, did indeed command this, he is doing it for that reason.

Regarding Rabbi Kook's words, I think the claim accusing the heretic of "wickedness" is patronizing and condescending. Although Rabbi Kook knew the discourse and debate around faith in his time (unlike the Haredi "greats of Israel" of our time, who live in a bubble), in my opinion it is not fitting to use such terminology, not in the study hall—and certainly not outwardly.

As for the words of Kovetz Shiurim and Rabbi Shlomo Zalman: Kovetz Shiurim holds that the commandments of a heretic have no value (except for commandments from which his body directly benefits; see there). And Rabbi Michi holds (elsewhere) that even his transgressions do not have full value.
From Rabbi Shlomo Zalman's words it appears that his commandments do have value.
And although at first glance it seems he is speaking only about one who is doubtful, that is not so. For if so, there would be no disagreement in his words with Kovetz Shiurim.
It seems he holds that the tiny doubt nesting in every person—perhaps after all he is mistaken—is enough to validate his commandments. And this also seems clear from his comparison to someone who is certain that the public around him is mistaken about the date and celebrating Passover on the wrong day. He is sure of himself, and still he would want to fulfill his obligation if they are in fact correct.
So if I have someone to rely on, it is Rabbi Shlomo Zalman and not Rabbi Kook.
In any case, following Rabbi Michi's answer, I asked my wife to say the words of kiddush quietly along with me.

With God's help, 7 Tishrei 5778

To Aharon—greetings,

In what you wrote in the second paragraph of your previous response, and in what you wrote in this response—"Of course my confidence is not absolutely absolute…"—you demonstrated Rabbi Shlomo Zalman Auerbach's point that even one who declares about himself that he is an apostate and a heretic, "there is still some doubt in his heart," and that is exactly Rabbi Kook's intention when he says that a person who is honest with himself cannot claim that his denial is certain to the point that there is not even "some small doubt" in his heart.

In any event, if with regard to your wife one can say that she should recite kiddush quietly along with you—when it comes to the children or guests, you obviously cannot suggest that they say kiddush together with the head of the household. There is no choice but to rely on Rabbi Shlomo Zalman, that they do fulfill their obligation through the kiddush of the head of the household, and Rabbi Shlomo Zalman is certainly weighty enough to rely on even not in pressing circumstances.

And with God's help, may the Giver of understanding help us be great "deists" 🙂

With blessings, S. Z. Levinger

As for the children, one could suggest the custom of the Jews of Hungary that all the sons recite kiddush together with the father. It seems to me that the reason for the custom was to accustom the children to saying kiddush so that they would not struggle with it when they became heads of households.

I really do not agree.

Let me explain again:

I did not quote Rabbi Kook's entire letter because of its length, but—
Rabbi Kook divides heretics into two groups. He looks around him and sees some who are doubtful, and some who confidently declare that they are heretics. In fact, it is clear from his words that many of the secular people around him belong to the second group. He applies to them the laws concerning heretics stated in the Talmud—"they are brought down and not brought up"—and according to his view they would not fulfill others' obligation.
The reasonable state, from his perspective (though not a desirable one), is doubt. But he recognizes and sees that there are many deniers who deny out of confidence, and he acknowledges this reality and accuses them that such behavior stems from wickedness.

Rabbi Auerbach rejects the very concept of "denial out of certainty." He claims that it is impossible for a person to deny with complete certainty. There is no such thing.
According to his view, a person who performs a commandment and knows that it is a commandment thinks to himself: in case the religious people are right, I have gained a commandment.
Did Rabbi Auerbach not know absolute deniers? He did. He is simply talking about a tiny tiny percentage of doubt that every person has. And because of that percentage, his commandments count as commandments. Therefore he rules that under no circumstances do we invalidate the commandment of a heretic.

That tiny percentage exists in every person in every opinion. Even if you, S. Z. L., are religious, you have a trace amount of doubt that you may be mistaken. That does not make you "undecided."
Baruch Marzel and, on the other end, Zehava Galon also occasionally think about whether their path is correct, and they too have the faintest shadow of a doubt whether their path is right. That does not make them "undecided" in their political positions.

Let us set Rabbi Kook's position aside for a moment. The purpose of my comments to you was practical: fine, with your wife you can agree that she will say kiddush with you, but what will you do with your children? And what will you do with guests? Will you ask everyone to say kiddush because you are a heretic and cannot fulfill their obligation, thereby embarrassing your wife in public?

Therefore my heart rejoiced when you found Rabbi Shlomo Zalman Auerbach's words that even one who sees himself as a heretic out of certainty can fulfill others' obligation because of the "some small doubt" that nevertheless exists in his heart. And since Rabbi Shlomo Zalman Auerbach's ruling is accepted in Haredi society, you can fulfill your children's and your guests' obligation in kiddush, and that is that.

With blessings, S. Z. Levinger

As for your claim that Rabbi Kook held that the deniers of his generation who claimed to deny with certainty fell under the category of "they are brought down and not brought up," the matter is completely contradicted by all of Rabbi Kook's writings and actions. After all, those were exactly the kinds of people the "pioneers" were whom Rabbi Kook drew close, many of whom had learned and then abandoned religion and rebelled. He held that they should be drawn close with love (see his many letters to Rabbi Dov Ber Milstein), and that their abandonment of religion came because they had not engaged deeply enough with the thought component of Torah, and also because religious Judaism had not sufficiently engaged in building the Land. See for example letter 561 and the article "The Generation" in Ikvei HaTzon; but the matter is lengthy.