There is a lot of confusion, which is understandable and I'm confused. I've been trying to get my head around it as well. I may be very wrong, but this is how I understand it:
I think what's confusing is people believing the use of 'woman' = female = single sex space now in all circumstances. But following discussions elsewhere, that doesn't seem to be true.
If you explicitly designate a service/space as single sex then you may allow only members of that sex in. You can use the term female or woman, but the important part is the use of the single sex exception under the EA. You can then deny access to the opposite sex. Any gender identity is irrelevant.
Alternatively, a provider can use the term 'woman/man or as Merrymouse says, 'masculine/feminine' or a similar term and have it cover actual women/men, trans people and anyone of either sex essentially.
They are not invoking the single sex exception, because they are not required to by law and they have chosen to remain unisex and 'inclusive'. So it is not a single sex space and they have not claimed that it is, even if their usage of certain words makes people think that it is or should be single sex. They are permitted to do this.
I think the second usage is what Merrymouse is talking about. I also think they'll likely do what murasaki says.