Really interesting thread. I'm Jewish on my dads side and my moms side but I'm also visibly black. My moms mother is a holocaust survivor and always tells me the first time ANYONE every considered her "white" was when she came to America. She's a dark eyed curly haired French Jew. When I was little people asked me what I was so much and I never knew what to say (My mom is half French Sephardi Jew and 1/4 French Catholic and 1/4 East African and my Dad is half Ashkenazi Jew and half East African). She would tell me the story of first going to the Caribbean and then to America and about "white people" in America and how they would call her white too, and how confusing that was to hear. Finally at the end of her stories she'd tell me to just tell the other kids I'm Jewish. Of course I did and probably confused them even more since I'm a medium brown colour with dark curly hair! I think it's natural for immigrant groups to want to associate with the dominate group in a population, and want to not assimilate into a group considered to be at the bottom. So it makes sense to me that very visibly curly hair and dark eyes was something that separated many from dominate culture. I see this with a lot of my Jewish friends.
I have rather dark skin for what people perceive should be the coloring of a mixed person, and even when I wear my hair curly I am often mistaken for Indian (from India). Most people assume I'm Hispanic or Indian or partly here in the states. In Europe 99% of the poeple I meet insist I must be Brasilian (as if they are they only mixed people around!) People tell me straight hair looks more natural for me, and it was even suggested to me by a Rabbis wife no less, that I straighten my hair because it would make me look less black and more Sephardic to increase my chances of finding a nice Jewish boy whose family would mind him marry me! Little did she know I'm looking for a nice Jewish girl!
Ethnicity is too complicated, moreso in American than anywhere I've lived, I just don't concern myself with it.