First of all, my wife is Chinese but born in and raised in Indonesia. She identifies as Indonesian; her father identifies as "Chinese Indonesian". When her brother married a "native", her mother asked him, if he wanted her to kill herself. Bigotry was huge in the previous generation. But after 40 years, her parents are beginning to become more Indonesian and less Chinese Indonesian.
My wife's brother is Chinese Indonesian, but far more Indonesian than his parents. His children are pretty much, Indonesian with very few vestiges of Chinese even though blood wise they remain half Chinese.
My wife is Chinese Indonesian like her brother, but very Americanized to the point she would not function in Indonesia, regardless of how she identifies. When she visits, she does not feel like she is going home, she feels like a tourist returning to a favorite place.
As an example, she would have trouble bribing the right people to get things done, but that is inherent in Indonesia. Two examples, that capture the culture view of things. During the OJ Simpson trial, my father-in-law stated US justice is strange. He said in both countries murder is legal. In the US, you can kill someone if you have really good lawyers, Indonesia is simpler, you just bribe the judge and cut out the middleman.
When I told him I thought bribery of public officials was corrupt, he said in America you "tip" waiters, why wouldn't you tip public officials. You can't be Indonesian if you can't think like one. You can celebrate your past, but it is your past, not who you are. Using a "biblical phrase", when you begin to assimilate and adopt the values of America, you become a "new person".
My father-in-law grew up in Indonesia, his behaviors are that of an Indonesian, not his ancestral roots from China. His ancestors lived in Indonesia for two or so generations, he identifies as Chinese Indonesian, likes Chinese food, but behaves like an Indonesian to the point of having served in the military for the first half of his career.
My children realize they have Chinese blood, and their mom comes from Indonesia, they like Asian food, preferring Korean and Japanese over Chinese and Indonesian. They also like Thai and Vietnamese food along with Hawaiian (which they think of as Asian like). Neither speak Chinese or Indonesian, but one speaks fluent Spanish. They have studies black history more than their own cultural history.
I did laugh when getting off a plane in Hawaiian, my one daughter said she was Hawaiian. I asked her why she felt that way... she said because the people here look like her. She has since moved on from that, but I think it is natural for people to identify with people that look like they do, which is why separatism is such a powerful force.
But circling back to my wife, even if she "self-identified" as Indonesian, Indonesians would not see her that way. They would see her as an American of Indonesian birth and treat her that way. Her old Indonesian friends do that when she visits her parents. She is still their friend, but she is not one of them.