Joking aside, I think there are probably two elements, namely:
(1) Critical mass/'safety in numbers'. At least one in every, what, couple of hundred men seem to these days see themselves as a woman. Many of the men who do this are eloquent, educated, men, from, I suppose, 'the ruling class'. So people listen to them. There are as yet no such safeguards for trans-racial people.
(2) Existence of a binary. Even though denying the sexual binary is an absolute favourite trans pastime (right up there with tweeting abuse in JL Rowling's direction), the very notion of being trans implicitly acknowledges the binary's existence, e.g. 'I wasn't male, now I'm female, you must at all costs treat me as female, treating me as male would be a hate crime'. But race doesn't really have a binary at all. There are obviously plenty of people, it's probably true of most people really, who you can quickly glance at and immediately have a really good go at deducing at least the majority components of their recent ancestry. But to the questionable extent that you can pigeonhole people into discrete 'races' there are certainly more than two, and e.g in this country there are plenty of very 'white' people who have non-trivial amounts of non-white ancestry (e.g. sub-Saharan African, Romany, etc etc)... so, y'know being trans-racial sort of can't really be 'a thing' in the same way that transgender is, since so many people really are a bit of a mix.