The intersection between religious conservatism and transactivism makes me very uncomfortable TBH
I understand the point about needing to understand how things like bathroom policies impact on all women, including those with a faith that precludes them sharing spaces with men without a chaperone, or the need to adjust clothing without doing so in front of a man
BUT
I don't want to use conservative patriarchal strictures in order to fight against TRA ideology, because I think it's appalling that a woman could be spurned by her family for having physical contact with a non-family male in a professional context. I oppose the hijab and the niqab, so it would be hypocritical of me to use them as a reason to object to unisex toilets where women might want to adjust their attire in a single sex environment
In relation to mosques, I suspect it's very simple in that they will simply ignore any TRAs that attempt to enter the wrong sex segregated space, and not particularly care about whether they have a GRC or not.
I do, however, really worry about the impact on girls from conservative backgrounds of young transwomen wanting to access single sex spaces in schools. Girls will be withdrawn from school to avoid mingling, particularly in changing rooms. We should, however, be fighting this on two fronts: one is keeping men and boys out of women and girls' spaces; the other is ending oppressive and sexist attitudes that tie women and girls to the home