Well, physically, an awful lot. Psychologically, maybe not so much. From what (little) I've read on the subject it seems that a lot of folks who go through this process have identified and felt as though they were born into the "wrong" body or "wrong" gender for quite a long time. Maybe it's just a mistake of genetics, a fluke, a wire or two that should have zigged when it zagged instead. I don't think the fluidity of gender itself has changed, but the ability to enable that fluidity has. Put another way, we finally have the means for these individuals to "properly" inhabit the body they feel they should've gotten in the first place.
Race is a completely different ballgame. You can't undo history, or ancestry, or wish away your progenitors. I can insist I'm a big blonde Swede all day long; I can demand someone recognize my authentic Korean roots; I can say I'm a Sudanese ex-pat all the livelong day. Insistence, appropriation, even admiration, does not undue your race. It's not an issue of won't; it's a matter of fact that you simply can't.