ButFirstTea, first of all, thanks for sticking around to discuss, I think it's healthy to hear both sides. But I'd like to take you up on one point, and also ask you a question.
The point is this - you wrote: "I don't think demanding equality and representation removes anything from anyone else." I think this is an oversimplification (and the fault of that wretched "equality is not like cake" meme). Sometimes rights come into direct conflict - for example, feminists' assertion that women should have a right to bodily autonomy which includes absolute control over their reproductive functions, up to and including abortion on demand conflicts absolutely with the religious right's assertion that foetuses have a putative right to life. Society has to step in at this point and reach a consensus as to whose right is the one that is going to be enshrined in law. Either you allow abortion, or you ban it. There is no middle ground. And someone is going to come out of the situation feeling that the law is wrong.
I think in some instances trans rights is parallel to this. Take, for instance, Danielle Muscato taking up a place in a homeless hostel, with the result that two homeless women were then forced to leave because their complaints about sharing private, intimate space with a transwoman were deemed to be transphobic. Either women have the right to determine what counts as women's space, or transwomen have a right to come into any space designated as "for women" - there is no middle ground.
The question I'd like to ask you is why you think that historically and geographically, across all cultures at all times in history, women have been systematically disadvantaged as a group? Do you think it's just an accident, an accident that's repeated itself over and over again? Or do you think the question is ill posed (and if so, why)?
Radical feminists have an answer to this - to borrow the phrase from police procedurals about motive and opportunity, it is because men are physically stronger (have the opportunity) and because they want to control women's reproductive labour (the motive).
A friend of mine was fired for getting pregnant. She's far from being the only woman in that situation. I had to take a past employer to court for equal pay (for the same job) - because long pay scales led to a situation where women who'd had time out to have children got left behind relative to men who'd sailed up the pay scale unimpeded - even though both sexes were doing the job equally well. Even friends who have no intention of having children have been asked in job interviews (illegally, but it still happens) whether they want to start a family - then the job's been given to a man.
And that's before we get on to sex-selective abortion (the clue is in the name - no-one asks the foetus what its gender identity is), or FGM, or breast-ironing, or female infanticide, or forced marriage. All these are done to women on the basis of their biology, not on the basis of their gender identity or their presentation.