. . . we don't permit them to change any wording or anything that has the word woman in it, because they aren't the right sort of woman.
No, we object to people changing wording because doing so eradicates women. It doesn't matter who does it, and there is no 'right sort of woman' other than in your head, or on the script you keep repeating.
Non-binary people don't exist because some people think it's just to do with dressing a certain way and they must designate themselves one sex or another even though they think it is none of your business.
No, wrong again. Non-binary people definitely exist, and comprise the majority of the population - the ones who don't give a flying one about 'presenting as' one sex or the other, and change their clothing style according to their mood.
Tranwomen are mostly men impersonating women in order to access their personal spaces and/or insinuate themselves into achieving something they couldn't as men.
Yet again, this is wide of the mark. Transwomen are men who would like to be women. Some of them believe that they have been born in the wrong body, and just want to live as though they are members of the opposite sex, harming nobody.
Some of them are autogynephiles, who get sexual pleasure from being mistaken for a woman, but are actually heterosexual men who want to have sex with women, so define as lesbian, but then get annoyed when actual lesbians don't fancy them (because lesbians are attracted to women, not men).
Others, however, are sex offenders who enjoy the power of being able to insinuate themselves into female spaces with no sanctions. Here they can frighten, assault or rape women very easily, as well as touch them intimately and commit acts of voyeurism. It is because of the fact that some men (only some) pose a threat to women that safe spaces exist. The clue is in the word 'safe'.
Oh, and of course there are the ones who want to win medals at sport, particularly when the sport involves superior strength, and when a male physiology is an advantage, which is why there were women's categories in the first place.
Women are not being oppressed by rich powerful mainly white men but by all of the above.
Two wrongs don't make a right. The fact that rich powerful mainly white men can be oppressive (to both women and other men) does not make the fact that other groups can also oppress women less troubling.
Meaningless bollox about intersectional feminism v an invented and inaccurate definition of gender-critical feminism
Not worth the candle, really.