Thank you @Sunflowersforever for your thoughtful post.
The starting point is the owner of the space determines who can use it. In the event that a transwomen is barred from using the women's facilities (e.g. toilet, changing room), the only way forward for her would be to bring a claim under the Equality Act. Only individuals who intend, are in the process of, or have reassigned their gender would be able to bring a claim. A transwomen who is indistinguishable from a natal women (i.e. passes, has had all the surgery), has transitioned for a number of years, and has a GRC would win her case. Whether other transwomen would win a claim for gender reassignment discrimination - it depends.
The specific factors and the weights applied to them to win a case of gender reassignment discrimination are not written into the act itself. And there have been very few cases on this issue. Looking at the few cases there are, it is clear the courts are reserving a lot of discretion for themselves and approach things on a case by case basis. And this makes sense. The courts are balancing the rights between a number of groups and the cases are being decided on the facts of the specific case.
There is no judicial authority for the proposition that a transwomen in possession of a GRC can legally demand access to women's spaces. It is possibly a necessary condition (although there are a lot of arguments it is not), but it is certainly not a sufficient condition.
Very roughly, to obtain a GRC today, a transwomen needs to have (or had) a diagnosis of gender dysphoria, have lived in role for 2 years, intend to live in her preferred gender role for the rest of her life and provided the required evidence to a tribunal. No medical transition is required.
So today a man could socially transition for 2 years, obtain a GRC and revert back to living as a male. In theory he could demand access to the women's facilities and bring a claim under the Equality Act. The reality is that he would be laughed out of court.
Likewise a transman could transition socially and medically, not apply for a GRC and then request access to the women's facilities as his legal gender is still female. Although some women might have been told he was trans and be perfectly happy to share the facilities with him, most women would be horrified by the thought. He too would not win a case.
The government has proposed simplifying the process of obtaining a GRC and removing the need for medical evidence. If the process in Ireland is followed - and that might be too radical for this Conservative government - then a statutory declaration would need to be signed in front of a solicitor or other Commissioner for Oaths. If the individual is dishonest in signing the statutory declaration then he can be sent to jail for up to 2 years.
An individual is free to change his mind later. But if he was dishonest at the time he signed the declaration - e.g. using it as device to commit crime - then he would be guilty of the offence.
The offences of Voyeurism and Exposure are both drafted in gender neutral terms, so a legal change of gender does not prevent these offences occurring.
Many transwomen don't have a GRC and it does not affect them day to day. However, there are times when legal gender is important and having a different legal gender to the lived gender - e.g. on DHS records - can cause confusion and stress.