Man =
adult human male
Transwoman = male human who says he is a woman
Therefore Transwoman = man who says he is a woman.
Which is fine, he can say whatever he (or ‘she’ if you insist) likes, but female only spaces are based on sex not gender so no men who say they are women should be allowed in spaces for female people:
We aren’t unnecessarily cruel though, hence advocating for third spaces for those males who would prefer to be female and the females who would prefer to be male (and anyone else else who wants to join them!)
Third spaces also provide facilities for male and female people who say they are neither male or female (aka NB people), whereas trying to cram men who say they are women into female spaces leaves NB people shit out of options.
Third spaces are best for everyone.