What are you on about?
Adult female. Not 'female who has gone through puberty'. For obvious reasons. Medicine is currently successfully fucking up some children's puberty, but has not yet thank God found a way to stop them growing up. A male child will not grow up to be an adult female, a female child will not grow up to be an adult man. This is nursery school level stuff. The amount of wangling and nonsense some adults will go through to pat male people on the head about their belief that they can be women just never ceases to amaze me.
If I worked with a transwoman I would treat her like a woman. I may well have worked with transwomen without realising that they are trans. If I found out I wouldn't stand in the doorway of the toilets saying "You're not allowed in here. You're a MAN!"
If you had had the experience you may be less naive about the not 'realising'. It's not about how successfully men can dupe women, it's about women's right and need to single sex spaces. If you personally don't feel you want or need single sex spaces yourself, how lovely for you, I am happy you have the luck and the privilege to be apparently completely innocent about the women not like you. There's a lot of them about though. You might want to listen to what they're trying to say before handing men those women's rights.
I doubt many women have stood in the doorway of a single sex space shouting 'you can't come in, you're a man'. Mostly out of fear. Many however will have just quietly had to turn around and go away and cede any access to give that special man his choice and self expression. The man won't stand there shouting 'All women who can't use this space unless it's single sex, piss off because I'm here and I don't care about you, and if you can't put me first you don't matter'. It's still what every man walking into a woman's space is communicating though. The women he excludes will mostly be silent and uncounted victims.
Why not champion the mixed sex third spaces that you would be happy to use yourself, and which give men an alternative to sex based spaces and still include provision of access for women who need single sex spaces? Why make it a zero sum game and sneer at those who won't play on your team?