Wow!
You say all of that, Vivienne as though you are unequivocally in the right. You are not. That's the point, the root cause of teh whole TRA debate!
Science is never unequivocal and certianly is not on sex and gender - mainly because the 2 terms are often used interchangeably, usually to mislead, and so a sentence including both of them never means the same thing to different readers.
Wopmen here have never said that transwomen need a GRC to use female loos. What is said, often, is that whilst women have been polite and turend a blind eye for decades, TRA actions have meant that many women are no longer willing to do so. So TRA demands, all the dennying of the possible ramifications of Self ID have damaged the relationship between women and transwomen. That is explained to posters like you on a dialy basis. Yet here you are repeating a twisted version of what really is posted to try and make your point.
Your point about Karen White is, as you well know through being on many of those threads, is NOT That he is representative of any/all trans individuals. But that he refutes the oft repeated statement that no man saying he is trans will be allowed / placed in a female space and go on to hurt women. It DOES happen.
How many MORE women will be sexually assaulted by a man saying he is a woman before you will accept that such men pose a real risk to women?
Mind you, your post as a whole reads very well, almost a text book case of double think and word salad. That you have to twist and lie to make your point just shows how poor a point it is !