Unusually, I find I'm in agreement with @alcovecupboards . What is this, the Twilight Zone?
Cupboards suggests a single-sex (women-only) service can exist side-by-side with an otherwise identical service that is for women and transwomen. This is logically possible.
Schedule 3 doesn't provide a sex-discrimination exemption for the latter. But imagine for the moment that you have created the former, with the usual Schedule 3 underpinning, but that now some potential users wish to share the service with men who have a female acquired gender as contemplated by the GRA.
They may believe wholeheartedly in gender identity theory. Or, in a weaker iteration, they may consider that the disadvantages of 'trans inclusion' (issues of safety and decency) are greatly outweighed by the advantage (mitigating psychological distress in the men), particularly as only a small number of men are involved.
I think this could only be justified if there is also sufficient women-only provision to meet demand. Otherwise you will run into problems with indirect discrimination as to sex (female) or belief (Muslim or Jewish) or even disability (PTSD caused by SA).
(The TRAs will kick off about the women-only service being transphobic, and come in anyway. How will you solve that, cupboards?
And some will complain that acquired gender is too nebulous, and you will get just any old man wandering in. But, they could have done this at any point in the last few years, and on the whole they don't. People do what's socially accepted, and that means at least popping on some lipstick or a skirt before entering the ladies, because it sends a readily understood signal.)
What does this mean for the OP's question? The users of the service are made up of:
Women who accept that they are women, and wish to share with men who claim a female gender identity.
And.
Men who claim a female gender identity.
The only thing these two groups have in common is a female gender identity.
It follows that the users of the parallel women-only service don't have a female gender identity, and this makes sense. Either they are transmen who have decided not to pop off to the gents, or they are women who have chosen the service on the basis of their sex and don't see what gender identity has to do with it.
So it's about belief. The woman gender service is for people who think that gender identity is important and that theirs is female.