Thank you for your thoughtful reply and question. Yes, the situation seems polarised, but also overwhelmingly in the gender-critical movement's favour, not only politically and with the media but also with the general population. Year by year, polls show an increasing number of women who are uncomfortable with trans women in women-only spaces like toilets (never mind far more controversial spaces like rape-crisis centres, prisons, and even changing rooms, where the views are even more trenchant).
Something I noticed in Bluesky discussions yesterday was a response to Jolyon Maugham of the Good Law Project, who was highly critical of the YouGov poll sponsored by Sex Matters and which shows the majority of the population welcoming the Supreme Court ruling. But two trans women responded with a compelling argument, telling Maugham he didn't understand how prevalent the gender-critical position in society is now, and that the YouGov poll is reflective of how things really are, regardless of how the questions are framed. Issues like sport were mentioned as being a luxury issue at this point; trans women are genuinely afraid and distressed by a blanket-ban on toilets (which I think is the women-only space that most trans women use). Whenever the trans community sees some chink of light, meanwhile, reality soon follows, for example yesterday evening with news of the Labour Party likely to stop trans women from being on women-only short-lists, which frankly speaking, seems really obvious to me following the SC ruling (which specifically dealt with women-only short-lists).
My own feeling is that Sonia Sodha in her last Observer article has probably identified the likely direction of travel, about the need for trans people to forget about women-only spaces and to focus on developing gender-neutral spaces, trans-centred services, trans-only short-lists, etc. However, the toilet issue (and to some degree, changing rooms in work places) remains a huge issue, because logistically most buildings are designed to expand and add rooms to cater for so small a demographic. I think most trans women will have no choice but to continue taking the risk of using women-only public toilets and hope nothing terrible happens. I think most trans women are far more afraid of men's toilets than women's, and would rather be called out in a women's toilet than attacked in a men's.
You say at the beginning:
"Seeing trans women as males is not inconsistent with a view that the law still permits them to use women-only spaces as a special exception, and Harriet Harman, for example, has expressed this view: it's not completely wild."
I would embrace this. I think many trans women would, at this point, and if not now, then certainly when the EHRC's statutory guidance comes into force. The gender-critical movement seems too well organised (Sex Matters seems to be running rings round any trans-advocacy charity) and their view of trans women too prevalent now. If most women are willing to use their statutory rights to assert their sex-based beliefs, and enforce and restrict women-only spaces to 'biological women' at places like the workplace and retail, then having a special exception for trans women for this most necessary of facilities seems like something I would certainly accept.