You know that men with a GRC are counted in the female stats and that most trans identifying men don't bother getting a GRC. This is your pivot get out clause: they're only trans now if they have a GRC.
A certificate can't work as a safeguarding protocol when nobody is allowed to ask for that certificate, which you can't in most day to day practical situations. A GRC proves nothing in relation to safeguarding. It's not a CRB check.
The Roxy Tickle case is ridiculous. The court was told that Sall Grover should have known Tickle was a 'woman' because the picture he submitted had long hair and a low cut blouse.
Woman = costume in Australian law.
I haven't introduced a pivot - the European Court of Human Rights did that years ago.
It's perfectly normal to have words that typify cohorts. Transgender women are men who like to do their thing occasionally. Transitioners are those who are undergoing a process of change. Trans women are typically those who have a GRC, although some trans women have undergone all of the steps but choose not to apply for a GRC, typically because of the spousal veto.
A certificate is not intended to be a DBS check. There's a process for that which applies to anyone. As a trans woman in the women's toilets, I don't know the criminal history of every woman that walks in. You need to ask yourself, why is it that you don't need to be concerned about cis women in the toilet, but only trans women. The risks are no different.
The risk assessment / safeguarding concerns are merely a rouse. The privacy concern is also a rouse, since the private space in a toilet has a door capable of being locked from the inside. There is no loss of dignity having to wash your hands next to a trans woman, and no increased risk.
I didn't mention Roxy Tickle - but you've raised her case because you object to her appearance. Do all women need to pass your standards test? Or just the women with a trans history?