I believe this goes on more than anyone knows.
Especially if a person is one "race or ethnicity" growing up and living around people of a "different race or ethnicity." People like to fit in.
I just found another famous example, this one a musician in the 1900's:
http://www.snopes.com/movies/actors/ironeyes.asp
https://youtu.be/j7OHG7tHrNM