I agree its unnatural for an identity to be purely based on phenotype, but its pretty rare that I will see people actually think of it that way. Race is almost always wrapped up in cultural elements and even if we ignore that I'm sure other elements would still be present such as descent from a common ancestor, immunity to diseases, innate ability to digest weird thing from their diet, etc. Notice though that this only reinforces the fact of just how French someone like Dumas is. It is a means of bonding people together in kinship just as much as it is a tool for the haters.
Phenotype does has a factor in self-identification, but its very limited and only happens for short periods of time when there is new contact until the normality of the differences is seen as a regular variation.
In order to create a white identity there had to be laws enforced on people to create such identity and even so, a lot of these laws outright failed, except in places where racialism was followed in a very zealot way, like in America.
For example in Mexico or Brasil where race laws failed, people don't see a blonde guy and a brown guy as different people, but they will see Asians and pure Africans as such.
Race relation to identity is correlative, not causative, people associate phenotype with identity because most people of a particular identity are expected to look a particular way, not because somehow the race is the generator of the identity.
Ill give a particular example of mine.
Im part Basque on my mother's side i look "white" enough to look like your average Spanish guy, I have international friends and i feel a much stronger connection to people from France or Spain than i do with Americans because the cultures are way more similar, most people i meet from these places don't feel foreign.
Ironically the only Spanish people i felt were foreign, were actually Basques, because Basques are a relatively different culture and they tend to be more introverted, ironically the same people that i probably share the closest genetic ancestry out of my international friends.
White and Black identity were created via slavery then segregation, if there had not been such segregation then America would be more like Brasil, where race would probably be an indicator of your social and economic class but not your identity.
