Yes they are different, cal. And that should be absolutely fine if they are. Imo, that is what we need to be aiming for.
As far as identity goes, I agree with naomi. If a Male is now a "woman" then I want a word for those of is who actually are. For all sorts of reasons.
Things are segregated by sex (not gender) often... toilets, meetings, clubs, changing rooms, sports, etc. Etc etc. All due to privacy, safety, comfort, competition, fairness and so on. Women fought very hard for those, even public toilets was a massive achievement.
Are we really willing to hand all those hard-won rights back to any man who wants them?