It would be useful for Sex Matters or FWS to have an easy to fill in, anonymous card system for women to register with them that they are a woman who does not consent to/cannot share a mixed sex space, and perhaps also whether they have a history of sexual assault from males. The numbers would be large.
The obvious brigading by activists wanting to fill out cards that they are very happy to undress in mixed sex spaces is fine if they would wish to do that, separate bag, but would be wholly irrelevant as yes, no one's questioning that, and the SCJ and everyone else is clear that mixed sex/gender neutral facilities should be there for those who want them. The issue is managing to tolerate the existence of the women who don't and can't use them and apparently needing help to be able to believe such women exist in society.
Another point to add to the advice of: Write Everything Down and Formal Complaint Needed Invoking Article 8 Rights: (on finding fire in progress, install your smoke alarm - thank you for that example!)
Women: your emotional response will be judged and used in evidence against you. (Gosh, it's just like in all judicial situations with women isn't it?)
The man's show of emotion has been unquestioned and taken seriously as evidence to be used against the woman.
I would say that demonstrating performative emotion and making sure the right people see it would be the obvious thing to add to the 'things to do if you want your rights to function equally to men's' list, but I actually have no doubt that the woman in such a situation would be disbelieved either way. Had she sobbed and collapsed on others as the man did, I would be willing to bet that this would have been seen as negative and reflecting poorly on her as much as that she failed to show sufficient emotion for the judge's liking. I would bet too that the authenticity of such sobbing and it's possible manipulative factors would have been thoroughly questioned and explored for the woman involved as they were not for the man.
Jeez the barriers women have to battle for equality in all areas. And the absolute nonsense it makes of pretending anyone believes these men are women. They are never treated like women. Never.