> A man claiming that he's a woman because he wears a dress and make-up and really believes he's a woman

Actually, my understanding is that it's really only the radical activists who insist on that sort of thing. Most real-world trans folks are sensible enough to grok the fact that while they might perform socially as their gender of choice, they don't in fact embody it in the same way as someone who was assigned that gender at birth would.