You've previously said that, "the organisations with decent legal advice seem to be changing their policies and signs, to provide female only, male only, and gender neutral facilities."
1. How widespread is this change?
2. Do you have any examples of facilities that have undergone this conversion?
If service providers are breaking the law by allowing trans men to use the men's restroom, then does that put pressure on the service provider to deny trans men access to the men's restroom, regardless of whether they offer a gender-neutral alternative?
I know you're asking seanie, but I'm going to play translator here, because I've had a reasonable bit of exposure to the ways in which UK and US differ, as well as some fairly in-depth review of the UKSC decision on this.
First off, let's hit some cultural differences: In the UK, most stores/businesses/etc. (collectively buildings) already have womens, mens, and disabled bathrooms. In the US, most of our buildings have a disabled-accessible stall in every mens and womens room, but that's not standard in UK. Similarly, in the US, we conventionally give disabled people first-call and priority access to disabled stalls if there's a line, but anyone can (and does) use the big stall if there's nobody waiting. In the UK, however, there's a lot of social stigma around non-disabled people using the disabled bathroom, since they're usually stand-alone single-use rooms. They pretty much treat the disabled bathroom the way we treat disabled parking - they're exclusively available to disabled people, and if someone non-disabled uses them they're going to get nasty looks at a minimum.
Another really material difference between the UK and US is that the UK actually HAS codified legal protections for women. They actually have constitutional equality which the US does NOT have. But they also have very clear guidance associated with that equality, that explicitly allows that in some cases, it's both legal and appropriate to limit access to some services or spaces on the basis of sex, because doing so serves a higher goal of either broadening equal participation in society (such as quotas for female positions on some boards or political positions) or becauses it serves as a safeguarding and protective measure that reduces the disparate level of harm that women face as a result of male violence against women. Thus, it's legal to have female-only restrooms, changing rooms, showers, rape shelters, and inpatient accommodations. That's something that the US doesn't have, in large part because
women still do not have equal legal status in the US.
Over the past decade or so, some activist organizations (stonewall predominantly) have been 1) lobbying politicians to interpret "sex" in UK law to mean "gender identity" and 2) convincing companies and other organizations that it already means that. They've been responsible for convincing many buildings to assume that womens restrooms/change rooms/showers/shelters are legally accessible by any male who identifies as a woman, on the basis of their self-declaration of their feelings.
The UKSC ruling clarified that in law, "sex" means actual real biological sex. It does NOT mean gender identity, and it does NOT give males who identify as women the right to use women's facilities.
But the ruling also gave explicit consideration to transmen, and recognized that a well-passing transman is likely to cause discomfort and anxiety in a female-specific setting. The ruling allows transmen to use men's facilities when they feel it's more appropriate to do so. Thus a bearded boobless transman can legally use the men's toilet, the men's changing room, etc. They're also legally allowed to use the women's facilities, but they're not prohibited from using the mens if that seems like the most reasonable and responsible thing to do. The ruling also allows that in some circumstances it may be allowable for a transman to be excluded from a women's service, but that it would be pretty limited. I believe the scenario referenced was of a rape survivors group therapy session, where the presence of someone who passes as a man is likely to be a barrier to the other women being able to talk about their experiences openly - but even in that situation, it was presented as a case-by-case situation, where if the other women in the group were okay with the transman being there, it was certainly allowed; if they object it would considered reasonable to direct that transman to a mixed sex or a trans-only support group, both of which are available.