Authority and decision-making in matters of thought

1. Your words about there being no authority in matters of thought (since they are a fact and not a norm) do indeed seem most appropriate (and even necessary). Indeed, many of Israel's great men believed this, and I tried to at least find an explanation for this. I have raised 2 possibilities (with questions), and I would be happy to hear your thoughts:
A. God, the Blessed One, changes His leadership and creation according to the halakhah that is established in our world. That is, God, the Blessed One, wanted us to decide on these issues and He will change the face of things according to our words. Accordingly (regarding His leadership), the opinion that we decide on the question of whether there is a Messiah for Israel is the one that will become correct. First, this does not sound reasonable at all and therefore requires proof. Second, in the Sanhedrin section, which is the sole halakhic authority, it is explicitly mentioned in which matters the Sanhedrin is approached: "If a matter is too great for you to judge between blood and blood, between case and case, and between us to deal with matters of dispute in your courts" (Deuteronomy 17:8). It should be noted, however, that in Jerusalemite the word "davar" is interpreted as the words of a legend.
on. Because we are dealing with extremely complex issues, there is a concern that the public will largely arrive at incorrect understandings, which are problematic both in themselves and in terms of the division of hearts and the disputes they cause. Therefore, God, the Holy One, has determined that it is incumbent upon the public to think that what is correct is what the majority of the sages of Israel think, for example, even though it may be an error in the perception of God's leadership or creation. At least statistically, this is what the majority will think correctly. Admittedly, this renewed perception requires proof. It is also not reasonable: it is extremely puzzling to think that God, the Holy One, would command us to deny the facts.
2. Another thing, assuming that there is no authority in matters of fact, what about authority in matters of fact that concern the act? For example, some claim that it is forbidden to ascend the Temple Mount for ideological reasons. Let's say they were to bring evidence from an authorized body (Gemara), is it obligatory to listen to them? Another example, if we bring evidence from the Gemara that according to the Tannaim we are at the beginning of redemption, and this requires certain actions, are we obligated to do so by virtue of authority even if we do not believe that this is the beginning of redemption? And so it is with matters of fact that concern the act, not just the explanation (such as the issue of fulfillment).