Those with genuine gd will still use the female facilities because no matter how great, kind and logical you are, you cannot reason with a mental disorder. They have no more choice in it than an anorexic does in starving themselves.
This is completely flawed. There are people with genuine dysphoria who use the facilities of their sex. To say it cannot be reasoned with is to ignore the fact that there are sufferers of GD who have come to terms with reality and put that into practice.
It’s also remarkable that you draw parallels with anorexia. We do not allow children with anorexia to starve themselves. We admit them, contain them and restrain them if necessary (legally not literally). We do this so treatment - feeding and psychotherapy - can be initiated to help a child come to terms with the fact that their body is healthy and does not need to be starved. It’s the exact opposite of what happens with children with GD, who make threats about their bodies, are certain their bodies are wrong, but instead they are told by adults that they are in fact right and they need to embark on medical treatments. To draw an analogy with anorexia, it would be as if a starving teenager is given appetite suppressants and calorie restriction to help them achieve their goal.
If children who had such distressing GD were treated like the anorexia patients - admitted, supported, intense therapy, prevention of harm, help accepting the realities of life - then they would end up in a much better place.
Do I think there is a level of fetishism/predatory and attention/control seeking behavior that has infiltrated transness? Absolutely. Do I think it's a huge problem? Absolutely not. It's a tiny minority of what is already a tiny minority, and if these people are going to do it, they're going to it regardless of how many GD transwomen we kick out of bathrooms.
You say it’s a tiny majority of a tiny majority: how many cases does it have to be before you would be concerned? You’re using the “rapists gonna rape” argument. The fact “rapists gonna rape” is the reason we segregate by sex in the first place. It reduces the size of the loophole. It doesn’t close it completely but it shouldn’t be widened. Your using the very reason why spaces should remain single sex to explain that it doesn’t matter if they become increasingly mixed sex. It makes zero sense.
And these predatory men will find it easier to perpetrate these crimes if it becomes unacceptable and/or illegal for women and girls to challenge the presence of a male in their space at that time. At this very moment, if I see a male following any of my DDs into a single sex space I will challenge them. The more that self-ID is perpetuated and challenges to such are shouted down as bigotry, the less able people become in challenging behaviour they may see as inappropriate. No one can explain how anyone is meant to tell the difference between someone with genuine GD and a predatory male. If preventing males, regardless of their genuine GD status or not helps reduce problems then I cannot see how anyone with any empathy would object to that.
To stop predatory men attacking women and girls isn’t easy, but I’m damned sure we shouldn’t be making it easier.