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Can a person not be committed to the Torah without deciding to be part of a community?

He is obligated (and not only can be obligated), because he is a part of the public against his will. Perhaps he is not aware of this.

In the Rabbi's Pardon, Rabbi Shlomo Fischer mentions Rabbi Kook in the context of accepting the nation, in part 2, section 15, p. 11, at the end of note 3 (cited in "From Sinai to the Gazit Office," p. 204, note 403): "And I found the basic body of accepting the nation upon themselves in the precious Adar." And see there on pages 199-205, which loaded this possibility (that accepting the nation is the source of the validity of the rabbinic commandments) into the words of the Ramban in the Roots.

Indeed. This is a rare place for him, and even there he mentions the book without the author. Probably in the hope that the ultra-Orthodox reader will not recognize it.

There is a point here that I am apparently missing. It is true that he is part of the public factually, but why does that entail an obligation to accept their understanding? What is the problem if every individual does according to his understanding? Is it because in the public's opinion this will exclude him from the rule (since he will no longer be defined as observant in their opinion)? And if so, what does it matter, if this is his understanding of the word?

I hope I have been understood, I feel that the wording lacks sharpness but I fail to understand the source of the obligation here.

It's like the obligation to uphold the law. There are issues where there is no law and then everyone can do whatever they want. But when there is a law, there is an obligation to uphold it. Why? Because I am part of the public whose representatives established this law and it is as if I myself established it.
The same is true of halacha. In issues where there is no problem for everyone to do what they want, there are no halakhic obligations. But when halacha has established something, it apparently does not want everyone to do what they want.

I didn't understand why when the generation after the Talmud accepted it. It forces me. And my ancestors accepted it at Mount Sinai?
What is the definition.
What is the validity of ” acceptance by the public” ?
I am part of the public only because in important matters we think alike. What obliges me?

When the public accepts something, it binds everyone included in it. This is the basis of all commitment to state law and the regulations of various guilds and groups. You are part of the public not because of what you think but because you are part of it. It is like being part of a family not because you think like the family. It is simply a fact.

Shalom Rabbi
Is it possible to say that even the faith itself, the 13 principles of faith, which are actually positive commandments, I am the Lord your God. And the prohibition to reflect on the principles of faith, which is a prohibition even if it is a Torah, as the Rambam writes in the Laws of Idolatry – we are obligated to them by virtue of accepting the nation. And then it turns out that the answer to the question why do I believe? Because it is a commandment. But this is not a circular argument, because what actually obliges me is accepting the nation. In my opinion, this is the position of Judaism and its sages. They never investigated the faith from the outside, but sought to prove that it is true and to refute claims against it. And as long as there is no absolute proof without a reply, I am obligated to accept the nation.

There is a logical bug here. There is no formal authority regarding facts, and the principles of faith are facts. Search the site for formal and substantive authority. The commandment of faith to act is itself a groundless matter, and you are here to build on it?! Your surety needs a surety.

The Rambam's words on the law of idolatry have been brought up several times on the site. I will quote again:

4 And it is not only idolatry that is forbidden to be pursued in thought, but any thought that causes a person to uproot the essence of the principles of the Torah - we are warned not to bring it to our hearts, and we will not be distracted by it and think and be drawn to the thoughts of the heart: because a person's mind is short, and not all opinions can reach the truth about his own desires; and if every person is drawn to the thoughts of his heart, he will be found destroying the world according to his short-sightedness.
5 How: Sometimes he will abandon idolatry; and sometimes he will think exclusively about the Creator, whether He is or not, what is above what is below, what is before what is behind; and sometimes in prophecy, whether it is true or not; and sometimes in the Torah, whether it is from heaven or not. And he does not know the qualities to judge by until he knows the truth about his desires, and he will be found to be coming to terms.

And on this matter the Torah warned, and it says in it “And do not turn after your hearts, and after your eyes, after which you are prostitutes, after them” (Numbers 15:33)– meaning that each of you will not be drawn after his short-sighted opinion, and imagine that his thinking reaches the truth.

Our Torah is a national, popular Torah, it is not intended for the wise only. It was given to the people. For the wise and the foolish, for children and the elderly. If everyone went outside of a mental state and examined all the religions, beliefs, and heresies in the world, there would be no Judaism. Rather, the Almighty used the mechanism of the national obligation to obligate all generations in every aspect of the commandments, which include the commandments of faith. And when there is a question, it is a mitzvah to examine, but one must ask the rabbi. The great men of Israel. And not to ask every question of all the priests and sheikhs, idolaters, and heretics in the world. That way, it is impossible to create a believing nation that adheres to it’. And I will make you a great nation, a holy people, it is said, not a great religion. In my opinion, this is what has sustained Judaism for generations, with the intellectual and philosophical reinforcements of the great men of the generations, Maimonides, Rabbis, and so on, who removed the obstacles to faith. But research in Judaism is always a second floor above accepting the obligatory faith. In my opinion, this is very legitimate. In the war against Hamas, we do not check whether they are right. Although there are such opinions today. Because every nation is obligated to its nation. And whoever does not is betraying his people. No Russian joined Ukraine in the war. National love is natural. And faith and the Torah in Israel are the foundation of our national and historical life. Therefore, abandoning the Torah is a national crime and an exception.

In a similar matter regarding the issue of the rape of opinions in faith.
Are you familiar with the words of Rabbi Kook?
Letters of Evidence Letter of K
Know that honest interpretation is always a great foundation in law, and this is true in both practical and theoretical laws. Therefore, we always need to reach the center of honesty, and if you show us a contradiction between truth and truth, then there is something decisive here, and this is a place for new learning. Thus, we will see in the matter of the law of freedom of opinion, which at this time corresponds to the majority of those with opinions in the world, how far its limits will reach according to reason. Lest you say that it has no limit, you will not be able to say so at all. The first is that we do not have even one measure in the world that does not have its extremism, and the nature of the matter requires that there is a limit to freedom of opinion, if it does not No limit, so that the yoke of any agreed morality will be broken, until he reaches in his private understanding the end of the opinion on which he stands, and then the earth will be filled with desolation, and a complete narrowing between opinions and actions will not be done at all, because actions will either lag behind opinions by a great deal or a little. So for example, if a person agrees in his heart that there is no yoke in murder, he is certainly a sin, and if this agreement flourishes, he will destroy the existence of the world, and so on. Thus we learn that there is a limit to freedom of opinion, but the difficult thing is narrowing the limit. And it turns out that the restriction cannot be exactly the same in every human society, because for example, the complete agreement in the heart that there is no loss in going naked in the market, for those who agree so, and claim that they will behave so in practice, is a sin among us, and should be a sin, and is not a sin among the savages in the Guinea Islands, for example. And since there is a difference between society and society, the difference will not stand at one place, but will be gradually divided according to a multitude of conditions. And in the case of faith, there is a great difference in this between Israel and the nations. If there were any people in the world whose very being as a people and its existence would depend on some opinion, then there would be a complete permission and also an obligation that in the case of that opinion it would not find freedom of opinion among them. Because this is not freedom but laziness in protecting itself, for some tendency to irritate the nerves of private individuals. It is true that sometimes there will be individuals who will be able to rebel against their nation, when they find that the same opinion, which unites and sustains their nation, is harmful to all humanity, so they will abandon the nation for the sake of the truth. But if the opinion that strengthens their nation is an opinion that does not lose at all, and if there is another opinion that is promoted outside its borders, and the body of the nation becomes the basis of its life, then there is no room for patience, and their patience in this is worthy of internal contempt from the entire nation and from all people. Therefore, when there is no other nation in the world, for which the proclamation of the name of the Lord in the world, as the eternal God, the keeper of the covenant and grace[2] and all the laws of justice, which are the measures of the Blessed One, will be the basis of its national life, and a special condition for its establishment on its land and the establishment of its government. And so there are such conditions in it that it cannot exist without these great opinions, and every greatness in the soul is associated with its corresponding shortcomings, and certainly Israel also has such shortcomings that bring them to the great necessity of carrying the name of God in their general content. Therefore, whoever causes in his opinions, and therefore in his actions, a weakening of the opinion that animates the nation, is a national criminal, for whom forgiveness is a curse. And in the whole world we have no example of this. The national content of any nation and language in the world is not at all connected in the nature of their existence with the opinion of the name of God within itself and in the world, nor with the generalities of any faith. And if there is a single people, with a base faith, whose faith is national, it is certainly so small that its spread itself would bring obstacles to all humanity, and even more so that it would not be able to exist on its own, then that people itself is doomed to extinction, the obligations of its existence cannot be demanded from its individuals. This is the basis of true jealousy of God, whose owners deserve to be given a covenant of eternal priesthood, in distinction between the puffed-up zeal that comes from a lack of understanding and weakness of power.