You wrote that the local rabbinic authority has authority over the community that accepted him upon itself and anyone who belongs to it. The question is whether I am attached to a community against my will if I was born into one ethnic community or another, or perhaps communal affiliation is determined by a person’s desire to belong to a certain community?
Also, I understood that Rabbi Yosef Karo has the status of local rabbinic authority in the Land of Israel. Does that mean that everyone who lives in the Land of Israel is obligated to follow his rulings?

Nowadays it is customary (unlike in the past) for a person to belong to an ethnic community based on his ancestry (=his father), and from there he takes his customs. When we are speaking about a community, that is certainly the result of a choice and a decision to belong to it. In every place there are several communities, so the place does not determine it.
The claim that Rabbi Yosef Karo is the local rabbinic authority here is absurd. Rabbi Ovadia did indeed used to say this, but nobody really gets excited about it, and rightly so. There is no such thing as a dead local rabbinic authority. I have never heard of such a bizarre concept.

For the halakhic source of the concept “leading sage of the generation,” see my revered father’s book, part 1, page 84 — it can be accessed here: http://www.eretzhemdah.org/data/Uploadedfiles/ftpuserfiles/books/government_and_country/1.pdf

Regarding “a dead local rabbinic authority” — the meaning is that there are places that accepted upon themselves the rulings of a Torah scholar even after his passing. See here:
Responsa of the Rashba, part 1, siman 253
And in this way, anywhere they have practiced conducting all their actions according to one of the great halakhic decisors — as in a place where they practiced conducting all their actions according to the laws of Rabbi Alfasi, of blessed memory, and in places where they practiced conducting all their actions according to Maimonides’ code, of blessed memory — these great authorities have been made like their rabbi. However, if there is there a scholar who is wise and fit to issue rulings, and he sees grounds to forbid what they permit, he follows the prohibition. For these are not literally like his rabbi, since in the actual presence of his rabbi, were he to act not in accordance with his words, he would be treating his rabbi’s honor lightly in his own place.

When I said there is no source, I meant a primary source. Regarding a religious court’s power to confiscate property, there is a source (at least according to the views that this refers to the supreme religious court of the generation). But I know of no source for general authority vested in the leading sage of the generation. Indeed, some of the medieval authorities wrote this without citing a source, but the idea is puzzling. From where does this authority emerge? After all, the authority to confiscate property proves the opposite: that authority was granted specifically for that, and not for all the other powers of the Sanhedrin. Otherwise, what distinguishes the Sanhedrin? And the Sefer HaChinukh’s words are well known, but puzzling and not agreed upon. Perhaps the authority is as Rav Kook wrote, based on the agreement of the Jewish people, which is like the authority of the Sanhedrin — but then again, we are speaking of agreement, not authority. And where there is no agreement, there is no authority. By contrast, if there were halakhic authority vested in the leading sage of the generation, it would not depend on agreement (just as the authority of the Sanhedrin does not depend on agreement). The practical difference is that even if you hold that a certain person is the leading sage of the generation, you still have no obligation to obey him — and that is indeed the situation in our time regarding those who are accepted as the leading sages of the generation. Some of the medieval authorities also wrote that the supreme religious court of the generation can impose corporal punishments, but there is no source for that either. It is simply an emergency measure (in their view), not a law derived from any source. And as for a place where the custom is to act in accordance with one decisor, the words of the responsa Zikhron Yosef (by the son of the Rosh, also cited in Kovetz Shiurim on Bava Batra, if I recall correctly) are well known, where he wrote that this has no binding force (at least in a place with a local rabbinic authority, as you also brought here from the Rashba). In any case, we are not speaking of “the locale of Maran” because he was the rabbi here and has authority, but at most of a custom that they accepted to act according to his opinion (and not an obligation by virtue of authority). The practical difference is that the same mouth that forbade (=the public) is also the one that permits, unlike a situation of halakhic authority. In any event, here in the Land of Israel this is not the case. Even in Rabbi Yosef Karo’s own time they did not practice here in accordance with his view.

“The claim that Rabbi Yosef Karo is the local rabbinic authority here is absurd.”

But elsewhere you wrote that when I do not have a position in Jewish law, I should follow Rabbi Yosef Karo. Why can’t I follow whomever I want?

Because the custom is to follow him.

And what is the source for the idea that custom is what obligates?

Are you asking where we get that one should follow customs? In the straightforward reading of the Talmud, chapter “The Place Where They Practiced,” this is learned from “do not forsake,” and some derive it from vows. You can find surveys online.

So perhaps we should say that one must follow those leading sages of the generation, since that is the custom?

That is not the custom. Some people mistakenly think that it is an obligation, but it is not. And others do not do this at all.

Rabbi Elchanan Wasserman, in his book Divrei Chakhamim, wrote in an attempt to prove that even today, if most of the leading sages of the generation issue some ruling, there is an obligation to obey them just as one obeyed the supreme religious court in Jerusalem (under the law of “do not deviate”). See there.