At the moment, I would say "social pressure" is what's stopping them for the most part, but that is rapidly being eroded (see, for example, Travis Ablanza and the Top Shop changing room debacle - Travis is a non-binary individual who has tweeted about how much they enjoy going out dressed as a "sexy teen").
At the moment, we don't have (as has happened in the USA and Canada) cases of trans-identifying people with penises in communal open-plan changing rooms, but again, this appears to be down to social pressure. Up until very recently women could have objected and known that the law was on their side - now it is becoming very doubtful whether, say, a gym chain would actually be prepared to invoke the provisions in the Equalities Act (and various people have spoken openly about how the Equalities Act is the next piece of legislation on the list for change after "streamlining" of the GRA - it looks suspiciously like "rubber stamp the changes to the GRA by claiming it's just an administrative change, then alter the Equalities Act so the protected characteristic is gender identity in place of sex.")
So - at the moment do you think I would be within my rights to complain to the management of my gym were a fellow gym user to strip off next to me in the changing room and reveal a penis? And will I still be able to complain if changes to the GRA go through?
At the moment, does Karen White have a case to go to court about being removed from a women's prison for sexually assaulting two of the women inmates? And if changes to the GRA go through, and Karen White wanted to go through the new streamlined procedure of applying for a GRC, what evidence could be adduced to show that Karen White was not in good faith?
I want to know how the law is going to protect the single sex spaces currently allowed under the Equalities Act. Just hand waving and waffling doesn't cut it - I need to know the actual legal criteria (or to have someone have the balls to say "Actually there are no such criteria, haven't been since the GRA was passed, you've all been duped and single-sex spaces ceased to exist legally right back in 2003, just no-one noticed because it was all done under the radar.")