The simple answer would be 'fine, go use the third spaces so you're not using the facilities for your sex that you are so uncomfortable with, and the women who consent to join you and support you in this belief can come in there with you and you can all believe it together won't that be nice?'
That would actually mean equality of facility and resource for all, mutual respect for different beliefs, that the words 'inclusion' and 'kind' and 'diversity' and 'intersectionality' actually meant something instead of being code for 'woman submit and enable my manly self!'.
Do try that one on Reddit.
You're not allowed to not consent. If you have trauma - get over it. (the men don't have to, the men will be enabled in their feelings all day). If you're a lesbian, 'learn to cope' with straight sex, because the man feels entitled and you're just a woman, who are you to go looking for pleasure yourself or reciprocation, just provide the free sex work and learn to take it without a fuss. (I actually want to call a crisis team for someone dysfunctional enough to say that out loud and expect to be taken seriously, but it's been said many times. For real.) If you can't or won't submit to getting your kit off for men (look at the Darlington case at the moment, how the woman with childhood trauma was spoken to), it's your fault, and you don't deserve a space, you can just go without anything at all and serve you right for being subhuman scum.
You're never allowed to mention the fetish/porn/sexual aspects of this either, even though many women have the stories of their own experience and you can find plenty of sites where men are openly discussing it and enjoying discussing it with a large box of kleenex, often with pictures and videos.
As pp says:
trans equality of rights and no more
women's equality of rights and no less .
And that includes accessible spaces. Which means man free. End of.