Unfortunately, the known decades of data on paraphilia clusters are probably relevant here.
It makes no difference. Anyone who says they are trans are trans, anyone who has those feelings at any time is trans, that is the rule. There is no 'true trans' or 'false trans' which means inevitably there is a vast diverse spectrum in the population from 'felt like this from early toddlerhood' to 'late adult transition out of the blue' to 'sexual interest escalating over time' to 'it's useful in the moment for an agenda'. The bottom line is: this population not only does contain sex offenders, to whom presenting as a woman gives access to their victims; an unusual amount of this population would appear to be sex offenders.
It confirms how unreasonable it is therefore to enforce this population's right to be with and use women in a state of vulnerability and undress, over and above the women's right to privacy, dignity, consent and to be regarded as equal humans as opposed to walking male therapy resources, upto and including sex aids. As with the prison situation, the whole leverage of 'you must not say no to these multiple very serious serial rapist males torturing women in prisons because what if, because of a blanket policy, you said no to some poor mythical fraudulent, gentle souled accountant TW?' is just to destroy women's equality or humanity against the needs of men to use them.
Sod that. If women wish to go and strip off in third spaces to validate male people or because they do not care where they undress, then more power to them. Go for it. Those women are consenting, their bodies and their choices. But women who do not consent to this are not any lesser in importance to the male people stamping their feet because they don't want the consenting women, damnit. They want to control and abuse and dominate the women who say no to them and make it clear who's boss.
Which confirms any further if you had any doubt that these male people are not in any kind of good faith and should have heard 'not on your bloody nelly mate' a hell of a lot earlier.
But it's all irrelevant anyway, because even if every single TQ+ identified male was proven beyond all doubt to be a gorgeous, gentle, caring individual who was absolutely safe for women to undress alongside.... the fact would still stand that some women cannot use that space with any male, lovely or otherwise, and that male is excluding them from anything at all to meet their own need for freedom of choice - and that prioritises male choice and freedom over female access and inclusion. Male supremacism. Absolutely unjustifiable exclusion and subordination of women for male benefit, and those women are tax payers, so NO male people can use female single sex spaces at all. End of. This can't happen. The first job of women's spaces is to be accessible to all women.
And anyway, if that male person actually was lovely, they would care about 'other' vulnerable women with inclusion and access needs as they would see it, and wouldn't selfishly exclude them by seeing their own wishes and needs as more important.