@Munkeenut
I think it's far more complex when people 'ethnically identify' differently to how observers would categorise them because race has less biological basis compared to sex. Ethnicity is also not just about your genetics it's also about your cultural background. If you're brought up by black adoptive parents, grew up with black culture but have white skin then I can see why you'd identify as black (or at least African or Carribbean heritage). Likewise if you're Asian but were sent to a very white boarding school from the age of 5 and then onto Oxbridge then you may not consider 'Asian' as featuring as part of your ethnicity at all. There are also many people who don't look like their ethnicity - they look paler or more tanned than you would 'expect' given their parentage and therefore oberservers categorisations can be wildly off. The key question is whether these instances impact a disadvantaged and less privileged minority in the same way as appropriation might if the person truly identifies in a way that might be surprising.
Doesn't matter if you went to a 'white' boarding school and then to Oxbridge (which, by the way, is not 'white'), the world will guarantee to remind you weekly if not daily of your skin colour...
But yes, this is an illustration of how difficult it is to define people by ethnicity.