Curiously, the contemporary high profile cases of race and sex changes involve whites 'becoming' non-whites (Dolezal) and men 'becoming' women (Fauxcahontas, Jenner). These don't appear to be exceptions to prove the rule, either. There has been a pronounced flight from white evident in the US Census over the last several decades, and people from ancestries conventionally considered to be white, such as Middle Easterners and North Africans, are pushing for the creation of non-white categories to self-identify themselves as.
In 2004, the GSS asked respondents to choose from ten descriptors to answer the question "which is most important to you in describing who you are?" Respondents were also asked to select the second and third most important descriptors from the same list. Race/ethnicity was one of the options. The following table shows the percentages of respondents, by race, who identified race/ethnicity as the most important, second most important, or third most important aspects of how they identify themselves (n = 1,185):
Another option among the ten provided was gender. The percentages of respondents, by sex, who identified gender as the most important, second most important, or third most important aspects of how they identify themselves (n = 1,201):
Quite the conundrum. It's almost as if being white and being male, rather than conferring tacit benefits upon a person, actually has a deleterious effect on one's social status and perceived moral worth.
Parenthetically, these data are over a decade old. I suspect the white and male identification deficits are even greater now than they were then.
GSS variables used: SOCID1(2)(3), SOCID2(2)(3), SOCID3(2)(3), RACECEN1(1)(2)(4-10)(15-16), SEX