That is where things have to shift.
It's not unlike the battle Sarah is having for accessible rape services.
It has to be made clear to society and decision makers: this agenda will not accept equality for female people, or permit there to be a female space respected so that all females have equality of access. Even if there is a fully accessible, TQ+ friendly provision available.
And that's flat out unreasonable, discriminatory and misogynist. That's indefensible and eventually when reasonable people get this message and see it, they will shift the window back from 'poor you, use whatever space you are comfortable in' to 'only a git would block females from having equal fair access because they want to for their own political reasons, even after all their own needs have been met'.
That's when it becomes apparent this is anti-women, and extremist, and about intolerance of other beliefs existing in public. That's when the public support will shift. The only possible ending of this is that third spaces are there and available and it is re established that male people cannot use the specific female spaces needed by females for equality, access and inclusion regardless of how they identify. That if your own accessible facilities are available, you cannot block and remove other people's for your own personal control and satisfaction, like the dog in the manger in Aesop's Fable.
I know it feels like bashing our heads repeatedly against a brick wall, but this is not reasonable, and bit by tiny bit people are realising it.