Forget the sources and the ability to distinguish between the types of halakhot, and please answer the questions for me (at least 1–5)

1) Public acceptance gives it a status like that of the Sanhedrin. See Kesef Mishneh at the beginning of chapter 2 of the laws of Rebels.
2) Why should it? Its commentators already disagree with it.
3) They think that the public also accepted that upon itself. But as I said, in my opinion that is not correct.
4) “You shall keep My charge” and “Do not deviate.”
5) They have no such authority.
6) Kabbalah is not divine inspiration. The system of concepts and principles was transmitted by tradition (it seems to me that most sages believe this is from Sinai; I’m doubtful). From there on, these are interpretive considerations. But there is no problem using divine inspiration except where it contradicts Jewish law or decides disputes (“it is not in heaven”). Usually laws from Kabbalah do not contradict, and when they do, several halakhic decisors wrote that we follow the revealed law (Magen Avraham in the laws of tefillin and elsewhere).
7) I don’t know them. But I assume that there too he’s talking nonsense, as usual.

Thank you very much for responding.
I would like clarification on some of the answers:

1) Who decides what counts as public acceptance, and by what criteria? After all, in the time of the Talmud and afterward there were groups within the Jewish public that did not accept it (or rabbinic interpretation of the Torah בכלל), or that followed a different rabbinic source (the Jerusalem Talmud and perhaps additional halakhic sources).
2) In my opinion, it is not realistic to expect that the entire public must agree in absolute uniformity regarding acceptance of something, and only then it will be considered to have the status of a Sanhedrin ruling. Rather, there needs to be a critical mass for it to count as public acceptance (see question 1 regarding who decides and by what criteria). If so, then what in your opinion is nevertheless the difference between the Shulchan Arukh and the Talmud? In both cases there was not absolute uniformity, but acceptance of these sources was very widespread among the public (at least the rabbinic public).
4) The meaning of “You shall keep My charge” is to “build” fences so that the public will not stumble into Torah-level prohibitions. “Do not deviate” is the obligation to obey the ruling of the Sanhedrin, but on condition that they do not contradict the Torah, but rather interpret it and judge according to it. In the cases I had in mind, they completely uprooted Torah-level commandments (at least in practice), such as the bitter waters of the suspected adulteress and the heifer whose neck is broken, in the Second Temple period. So the question still stands: what was the source of their authority to change them?
5) Then why, instead of fixing things and restoring the crown to its former glory, do the sages continue perpetuating the breaches?
6) Quite apart from the question, in my opinion all of Kabbalah is based on divine inspiration. Kabbalah deals with metaphysical subjects that the human intellect has no connection to investigating there (philosophically and scientifically), such as: the purpose of creation, the roles of angels, the structure of the spiritual worlds, the ways the Creator governs, the meaning of the names of the Creator, the places of reward and punishment, etc. The grasp of these matters depends on a mystical connection with the spiritual world (prophecy, revelation of Elijah, revelation of various angels, revelation of the souls of the righteous, etc.), and the true kabbalists are those who experienced this mystical connection in its various forms. And as far as I’m concerned, it is very foolish to base a metaphysical worldview on speculative inquiry; either you rely on the metaphysical tradition of the Sages and the kabbalists, or you don’t. (I do rely on them, and the superiority of accepting their tradition rather than rejecting it can itself be grounded in reason with the help of logical arguments).

1–2. The Talmud had sufficient acceptance, in my estimation (I’m not aware of dispute about it, except maybe the Karaites). The Shulchan Arukh does not. Today it certainly encompasses all those who observe Jewish law.
4. That’s your opinion. The Sages thought otherwise. As noted, the Talmud has authority.
5. Where do they do that? They have no authority, and they didn’t do it either.
6. Then we have a disagreement.

I’ll let go of you regarding questions 1–2.
4) My interpretations of the terms (“You shall keep My charge” and “Do not deviate”) are not products of my own opinion, but the traditional interpretations according to the halakhic sources.
What does the authority of the Talmud have to do with this? I asked: what was the source of the authority of the Sages in the Second Temple period to stop Torah-level commandments that were practiced in their time?
5) I meant the repeal of decrees and enactments of the Sages not in accordance with the required rule (a court greater in wisdom and number), as presented in the book The Changing of Natures in Jewish Law by Rabbi Neria Moshe Gutel.
6) I assume you disagree with me about the superiority of accepting the tradition of the Sages and the kabbalists over rejecting it, and not with my arguments regarding the ability of the human intellect to attain answers to the specific metaphysical questions (that is, not only: is it plausible that there is a Creator of the world? etc., but assuming there is a Creator of the world then: what does He want from us? etc.).
That is the condition for the transition from deism to theism; that is, reliance on God’s revelation to created beings is the argument that gives validity to belief in the various religions.

4. No, they are not. The Sages’ interpretations are expressed in what they actually did. If they canceled laws, then apparently they understood that this too was transmitted to them in “Do not deviate” (at least according to Maimonides, for whom all rabbinic authority is derived from there, and this is not the place to elaborate). The authority of the Sages is to determine that this is the interpretation of the verses of “Do not deviate.”
As I wrote, I am not aware of Torah-level commandments being canceled by the Sages.
5. There are various explanations brought there, but it seems to me that the basis of it all is reason. If the times require it, the sages have authority to act that way. See section 4. I discuss all this at length in the trilogy I’m writing.
6. Indeed, I just don’t really believe in revelations to various kabbalists. Therefore I relate to the details of Kabbalah with some suspicion. The language and the basic intuitions definitely have value.

I think that if you want to continue the discussion, it’s better to talk about one question and be concrete (bring an example and we can discuss it). The general discussion is a bit slogan-like.

4) The commandment “Do not deviate” is a commandment imposed on the public to obey the instructions of the Sanhedrin.
Jewish law (tractate Horayot in the literature of the Sages) limits the duty of obedience. That is: the sages in the court are not allowed to do whatever they want—to uproot core commandments of the Torah—and if they uproot a core commandment, one does not obey them. In addition, even if they did not uproot a core commandment from the Torah, but ruled on Jewish law in a way that a sage qualified to issue rulings knows with certainty (according to the criteria established by the Sanhedrin) that they are mistaken, then he is forbidden to obey them.
After examining the sources, I obtained an answer to my question.
6) What I meant by “all of Kabbalah is based on divine inspiration” is: the metaphysical positions of the Sages and the true kabbalists (in my opinion), not every Kabbalah book ever written.
In my opinion, there is certainly room for speculative inquiry into kabbalistic writings (for us, as people who have not experienced the mystical connection with the spiritual world, we have nothing but our intellect in understanding the texts), and different sages interpreted kabbalistic texts according to their reasoning. My claim is: the main metaphysical positions that were transmitted by tradition (from the prophets to the Sages, some of whom at least had their own mystical connection with the spiritual world and were not merely conduits for transmitting the tradition of the prophets, as documented in the literature of the Sages), and the innovations that expanded and explained them (the Kabbalah of the Zohar and the Kabbalah of the Ari), are the ones based on divine inspiration. In my opinion, there were additional true kabbalists throughout the generations, including some who did not belong to the school of the Zohar or the Ari, but that school—the Kabbalah of the Zohar and the Ari—is, in my view, the main, most comprehensive, and most systematic one we have today, and it provides sensible answers (if you accept the assumptions of that tradition) to metaphysical questions.

4. You’re bringing us into the topic of one who errs regarding the commandment to heed the words of the sages, and this is not the place. It’s complicated and full of disputes and contradictions already in the Talmud itself.
6. You examined the sources and got answers about Kabbalah and what it is? Good for you. I assume we can’t get here into the question of the confidentiality of the sources (which sources did you examine in order to know how reliable the sources you examined are?). All that remains for us is only to clarify what the metaphysics of the Sages is, and who the true kabbalists are, and what their metaphysics is. After you examine the hidden sources and find the answers to that, you’ll be all set.
I also enjoyed the claims that X is a traditional Kabbalah “in your opinion.” It seems to me that a tradition is supposed to be transmitted and not depend on our opinion, but again, who am I to argue with the hidden sources.
Happy holiday

And it can be resolved by saying that the sentence “After examining the sources,” etc., refers back to the earlier point and is unrelated to the discussion about Kabbalah (the questioner asked how the Sages have authority to erase commandments, and from examining the sources he understood that they cannot)

Excellent. Indeed, definitely possible.

Hello A.H., indeed, you understood what I meant.
After examining the sources, I understood that the cancellation of Torah-level commandments by the Sages that I had encountered was regarding something within the commandment, not the whole commandment. And for that they do have authority, as it says: “If the court ruled to uproot the entire body of the matter…, they are exempt. If they ruled to nullify part of it and uphold part of it, they are liable” (Mishnah, Horayot, chapter 1, mishnah 3).
6) To the rabbi: I assume you meant that my use of the expression “in my opinion” was not precise, but rather “on my assumption.” If so, I accept the correction.

Anonymous, your words are self-contradictory.
If you are relying on the Sages, then how is the source you brought preferable to the very fact that they do indeed change the Jewish law? (assuming they indeed do so. And they do not.) Doesn’t that teach you that this is what they think?

I’m trying to understand the actions of the Sages through the rules of the Sages.
If I saw that in source X the Sages said that it is forbidden to uproot the core of a commandment, and in source Y I saw (apparently—and as stated, they did not do so) that they uprooted the core of a commandment, then I have a difficulty with them—not out of provocation, but in order to look for the consistency and logic in the sources of the Sages.
Example: the Mishnah in tractate Sotah (chapter 9) testifies that the commandments of the heifer whose neck is broken and the bitter waters were canceled in the Second Temple period (“When murderers became numerous, the heifer whose neck is broken was abolished… when adulterers became numerous, the bitter waters ceased…”); therefore I asked: how was there permission to cancel Torah-level commandments (apparently, the whole commandment without distinction or reason)?
However, in the Tosefta (tractate Sotah, chapter 14) there is a continuation: “When murderers became numerous, the heifer whose neck is broken was abolished, for the heifer whose neck is broken comes only in a case of doubt; now killers had become numerous openly. When adulterers became numerous, the bitter waters ceased, because the bitter waters come only in a case of doubt; now observers had already become numerous openly.”
So I understood that the tradition of the sages was that those commandments must be observed as long as there is doubt, but if there is no doubt then there is no obligation in the commandment, and therefore they had the authority to cancel it.