As hard as it is to believe, I don't really think that they think putting on a dress and having a surgery magically turns them into biological women. It doesn't. It does allow them to present, however, with the gender that their dysphoria pushes them towards. It's not something magical, but tragic and sad, and for which there is only an imperfect solution.
I also point out that I agree it's not possible to change your race. It is entirely possible, however, for someone from another country to immigrate here, live and learn our customs, and take a citizenship test. While they can't become an English descendent descended from the puritans, it is entirely possible for them to become, like the rest of us, Americans. That's also what makes us different from some countries, like Japan.
