No, we're not fucked.
There is no law that says men cannot access women's spaces, and there never has been.
Because it wasn't considered necessary. Social condemnation was sufficient.
Twenty years ago if a man walked into the ladies behind a woman everyone would've felt entirely confident in calling him out. Oi, mate, that's the ladies.
People don't feel like that now. They're worried that they might be misgendering somebody, or falling into some kind of terrible transphobic trap that they can't navigate.
Public perception has to change. The public must become aware that no, women's spaces haven't magically opened up to a special cohort of men.
That women have just as much right as they always have had to single sex spaces.
The tide is already turning, with all manner of sports federations making rules to preserve women's sport.
The EHRC is going to provide guidance for schools. They also need to get rid of the training children have been having in gender identity.
And, of course, the more people talk about this, the more everyone feels emboldened to act.
I think what women like me are trying to say is that the men who want into those spaces, are not the ones who are going to help you prevent it.
However reasonable they may appear, that's not the goal.