I suspect they are trying to fudge the issue, as nowhere that I could see on their web site to they advertise single sex service as allowed under the EA pre the Supreme Court ruling. ie is it "proportionate" to say that when booking overnight shared accommodation you are entitled to have this as a single sex provision.
They do say as part of their booking process you can choose to tick either male of female but dont appear to say what this relates to. But again if you just look at their web site there doesn't seem to be a Policy link.
So I am sure they are thinking we aren't offering single sex services, the supreme court may have said the word women means biological sex, but the Government hasn't passed guideline to say how service providers should implement it.
But they are totally guilty of not making it clear from the home page of their web site, that they are providing a service based on identity not sex.
And in doing this they are putting women at the very least at discomfort and at the very worst leaving women frightened and scared.
On any level as a service provider this is a disgrace.
Edited to add:
One of the common responses from not just the charity sector put also commercial providers that the organisation MUST be clear and honest about the basis of their provision.
The fact that they aren't implies far more about them than anything else