I think the biggest problem is that we're not talking about race at all, we're talking about cultures that are stereotyped with a race (or vice-versa).
I look Hispanic. Does that mean I need to identify as such? Not really, but I could if I wanted to. Does that mean I need to get in touch with a culture that is foreign to me? No. Do I need to learn Spanish for the sake of it being something "my people" do? No.
That's why people call me transrace. I don't agree with it because to me none of this is about race. I was born and raised in Southern California, so I consider myself American culturally and I try to avoid racial labels in general. So why call myself white if asked? Because when I say I'm Hispanic or simply look Hispanic, people treat me as something other than American. I get ads in Spanish, I get comments about Mexico, and so on. It's just easier to say I'm white since that's true (even though many would not i consider me to be) and that's why people have considered me transrace.
I really like everything you said, actually. This almost seems closer to my own belief than what I'm saying lol ---