I'm not following your thoughts here . . . who does not allow the option?
“Acting White” doesn’t go over well with a lot of Black people - all the old-fashioned cultural baggage of ‘passing’, the modern equivalent of somehow being traitorous, &c. And a lot of White people consider anyone mixed to be ‘Black’.
The family I referenced seems to have ignored all of this, and live as individuals, happily partaking of both of their cultures as they please. But with others, I’ve seen a lot of outside pressure on kids to identify in one direction.
I don’t personally believe in the concept of ‘race’. We’re all one species, cultured differently. But the Race Idea is alive and well, and used everywhere to divide.