Thank you. What about the rest of the questions?

As for facts, there is no obligation to any authority whatsoever.
As for Jewish laws that stem from an incorrect factual assumption, simply speaking, in my opinion those laws are void. But that is only if it is clear to you that those rulings really are based on that assumption, and it is also clear to you that the assumption is mistaken.
There are cases where the halakhic ruling can be "rescued" by giving it a different meaning.
When it comes to prayer (a blessing or thanksgiving), this is doubly true, since prayer is not just moving your lips but also directing your intention to the content, and when you do not agree with the content, then even if you want to comply with the Sages’ ruling, you cannot really pray.
All this is with regard to laws established on the basis of a factual or scientific conception. If you are speaking about laws established on the basis of a value-based conception (socialism), here there is authority and there is obligation if the matter was established in an authoritative text (like the Talmud). The reason is that even if you do not agree with the value judgment, this is not a factual error. Therefore the law that was established here is binding. But that does not mean you are obligated to adopt the values that underlie it.

Thank you for the answer. Do you have any article on the subject?

No. It will be in the second and third books of the trilogy.

In your opinion, Rabbi, should a person who prays on Independence Day in a minyan where they say Tahanun at the very least refrain from doing so, or is there some value in participating with the congregation? I mean, from the outset, a person who does not make a practice of saying Hallel in a minyan, and whose saying Hallel is only an act of goodwill and is not based on a halakhic conviction one way or the other. I assume that the opposite case would not even raise such a question—that is, a person who normally says Tahanun and happens to find himself in a minyan where they say Hallel would certainly not join them, because he disagrees with that view. The question is from the outset about a person who has no tradition or firm opinion on the matter (which fits the nature of this halakhic issue, where without education from childhood a person stands there wondering how in the world he is supposed to decide).

In my opinion it is preferable not to pray in such a minyan. Better to pray alone. Saying Hallel always rests on halakhic recognition. Do you mean to say that you are not obligated to say it and that it is only voluntary?
As for the second case, I do not understand how there could be a person who thinks it is forbidden to say Hallel. At most he simply does not have the practice of saying it (and even that I do not understand).
I do not see any need for education. It is a simple logical point that one says Hallel for a deliverance. As for a blessing, one can debate it, though even there I do not see a major issue either way.

Thank you very much. Yes, I meant that it is voluntary, because in my heart I do not feel gratitude here the way I do in other recitations of Hallel. That is a fact. There is, for me, something strange about this Hallel of Independence Day. So I say it without a blessing and hope that if there is some side of the heart that feels gratitude for the national revival, that counts. At the same time, my heart stammers on this issue. A bit like a person who asks in prayer and is not even sure that anyone is listening at all. Maybe… But the answer addressed my question. (In Haredi-Ashkenazi areas, generally speaking, there are no Hallel minyanim but rather Tahanun minyanim, and that is why I asked. In earlier years I used not to join for Tahanun, but I also would not say Hallel alone, because it felt artificial.)

What I said above about my past practice was of course only if I was not in a place where they prayed Hallel. I mean that I would not make a special trip to look for a minyan where they say Hallel—why should it be different from other prayers, where I do not do that either. Even if I missed a Zionist minyan and in front of me was a Haredi shtiebel where there were later minyanim as is customary, I would go there and not over-analyze the issue too much. My simple feeling was that I would separate myself from the congregation regarding the saying of Tahanun, and that in doing so I was not doing anything wrong. And it was that feeling that I wanted to confirm with you. Thank you.)

Let me just clarify two things:
1. In principle, one should indeed not separate oneself from the congregation, and therefore it is preferable to pray alone, and best of all in a minyan that says Hallel without Tahanun. There is room for the argument that where the local custom is outrageous and mistaken, there is value in separating from the congregation and not saying it even when they do. [After all, that is also what a Haredi person usually does when he happens to end up, heaven forbid, in a Zionist minyan. Of course, I am not talking about retaliatory actions, only giving an illustration.]
2. I think saying Hallel is connected not to feelings but to conceptions. If in your opinion there is something here worthy of Hallel, say Hallel. What is in your heart, in my opinion, is not relevant to the matter.