Um, why?

There is some pretty stiff anti-trans prejudice out there. Unless you end up hanging with the power-inversion justice-seeking crowd, if you look like a woman but claim you're a man, you're not going to get, on average, even as much privilege as you would if you were a woman claiming you are a woman. (If you hang with the power-inversion crowd, you'll likely get black-privilege, too, and woman-privilege.)

But if the trans man has HRT and top surgery and voice lessons if needed and dresses the part, and nobody can tell any longer that they weren't always obviously a man (they "pass"), then yes, they pick up all the social privileges of their apparent status.

But why wouldn't you pick up all the corresponding white privileges if you made correspondingly large changes to alter your physical appearance? Given the huge variety in appearance of people who are classified as white, it seems like if you went to the lengths that passing trans people do to pass, you would pass as white. How would anyone even know not to assume you were?

It just seems like you're overlooking how much effort and what drastic changes trans people often have to make in order to reliably switch how their gender is socially perceived.

And if someone was willing to go to that level of effort--not like Stefani, obviously--to be the race they feel they really are instead of the one that society says they are, why wouldn't we accept it to the same extent that we accept change of gender?

(This is all as a matter of principle. In practice, of course, it matters whether anyone actually has such strong feelings of racial dysphoria; if not, then the argument for transracialism becomes a lot less clear.)