My understanding:
A. Gender: society's expectations of a person due to their sex. (girls wear pink and are friendly and caring)
B. Gender identity: personality. (I like the colour green, I am a misanthropist and although empathic, quite lazy)
C. Gender incongruence: Not wanting to do the things that society says I should do because of what sex I am. An incongruence between A and B. (I like the wrong colours, clothes, hairstyles, I am not caring/friendly/girly enough)
Feminists say: That's fine, like what you like, sex has no bearing on personality. Also, if we could do something about male violence, that would be good.
Genderists say: If you have C then your sex is wrong and you must try to change it. Also anyone of the opposite sex must accept you, and make allowances for you.
This latter suggestion is okay until one notes that we are dealing with two sexes, one of which has almost all the propensity and most of the ability for violence and sexual violence, and the other sex has almost all of the vulnerability, including the risk of pregnancy.
For this reason, as well as cultural, religious and reasons of propriety, the female sex has fought to make and keep spaces for their privacy, dignity and safety where they can, say, get changed, receive medical care, attend to bodily functions, etc, in a space free from the males sex. Legally, this is described in the Equality Act.
Now, some people are suggesting members of the members of the less physically powerful and more vulnerable sex are to accept members of the more powerful and more risk-taking and more inclined to violence sex in the spaces reserved for the former sex, because some numbers of the latter sex has C - gender incongruence. (Or at least, says they have C.)
I do have sympathy for those with C. I think A should be questioned and challenged. I think B is about as meaningful as horoscopes and saying the French are hot-headed and passionate.
Most of all, I think women need and are entitled to single sex spaces and rights.