Hmm, I remember waiting for our turn at an exhibit at a science centre, where people had to input their characteristics. The little girl in front of us was very confused when it asked for race, there was an option that looked like her mum and one that looked like her dad, but none that seemed to fit for her.
There is a factual element to race, but it is not as clear cut as sex. Racial physical characteristics can be obvious or less obvious, people can have parents and grandparents from different ethnicities. People can be raised in one culture or another, can be adopted etc.
It seems like there are lots of good reasons people could feel an affinity to a racial identity they do not have.
Sex is much odder, I appreciate that people may not identify with the stereotypes of their sex, and we are told that gender identity is separate from traditional gender roles, masculinity/feminity and sex. Yet they seem to conflate it with changing sex rather a lot.
I don't feel I have a gender identity but I don't mind if others feel they do (I also don't have a football team I support and don't believe my horoscope means anything, however I do have a hogwarts house but I'm sure lots of people don't bother with that)- there are lots of spaces/situations in which sex doesn't matter, but where it does, we should go by biological sex not gender identity.I can't think of a use case for sex not mattering but gender identity being vital.