The concepts of race , ethic minorities and nationalities are defined differently in different countries and groups. There is a definition that goes by skin colour solely, an other by citizenship, an other by cultural heritage for example. And sometimes it gets very hard to determine what one can do and what not. Personally I would say, the life experience matters a lot and the cultural heritage. If a person, lived in a black community all her or his life, although he or she is asian or white, and is devoted to that community, I think it is legitimate, if her she identifies as black. An identification without devotion and experience in that community would be unfair to the "native" members of that community. On the other hand, nobody should be forced to commit to a country or nationality, just because coincidence made him or her belong to that race or ethnic group. If there is no inherent identification that person wants, than there is none.
As for me this is a very complicated question . Personally, race, ethnic things and nationally do not mean much, but it seems to mean a lot to others and not only in the racist kind of way, so that I have to deal with those things nonetheless.
By skin colour I am white, by citizenship I am Russian, but I live in Germany since I am 7. My dad is a Georgian and my Mom was Jewish, which in Russia is not solely a religion, like it is in Germany, but refers also to ethic things. Thus, although a person has a Russian citizenship, he or she is Jewish, when the ancestors are, even though he or she might be an atheist or having an other religion. (This is contrary to the version in the Halacha, where a person is Jewish when the mother is Jewish when the child is born and is either observant or not, if he or she has an other religion then judaism, he or she is out of the community). Moreover, sometimes Georgians in Russia are seen as non-whites, even if technically they are Caucasian and white.
So choosing something gets kind of difficult for me. Also I have faced a lot of criticism for not loving a country, namely Russia (or any other for that matter), because according to those people, a person is supposed to love the country where he or she is born in. Additionally, some people, see me as Jewish, due to the heritage and halacha rules, although I almost do not have any connection to neither the culture and especially not the religion. One time the expectations went up so high that I felt myself obliged to do research on ashkenazi Jewish things, and although I gained a lot of knowledge I am very careful to identify with those things, since I do not believe/do them and find it unfair to the very faithful devoted Jews, to identify with something that I did not live with and that has no more or less meaning to me than many other things.
And about ancestral experience, I do not it think always that matters. If it is not passed along, not told, not indoctrinated even, a child does not feel it or grow up with it. So I would not decide the ethic group through ancestors, only through personal experience and affections, if there are any. I am not saying that ancestral things should not be appreciated, but just because some belonged to some group, it does not mean, the daughter or son or anybody is obliged to do so.