I'm going to make a suggestion that probably no one will take me up on but: Watch the film She Said. It's available on Amazon Prime right now, perhaps other platforms. Not so much to inform you about the whole Harvey Weinstein issue but because if you listen to how women talk about how they were expected to tolerate behavior, to accommodate it, to work around it and how little any of that did in the way of protecting them. It's a small, very small taste of what girls grow up hearing, absorbing, incorporating into their behavior. Not to make a fuss. Not to expect to have boundaries. Not to expect to be believed. Just to expect and be prepared and to deal with it on your own. In silence.
Though I believe you genuinely do, I don't understand how you can care about the actual issue of sexual abuse of women by men in positions of power, and come to the conclusion that
trans women in gym locker rooms, who in terms of social privilege basically the exact opposite of a man like Harvey Weinstein, are the real problem here. You can heap whatever persecutions you like on trans women, and it will not make anyone an iota safer. Not women, not men, nor anyone else. They aren't the group most likely to commit those kinds of crimes, nor is it an effective approach to crime to just blindly persecute entire classes of people on the basis of what some of them have allegedly done, even if they were. By criminalizing the actions of the innocent while turning a blind eye to the crimes of guilty, we make things worse out there for everyone, not better.
Two things here.
First, if we accept your premise that transgender identified males represent no risk to women whatsoever and would never sexually assault or abuse women ever... We still have the problem of not being able to tell whether any given male-bodied person is a transwoman or not. Let me give you a more explicit scenario. Assume there is a locker room where women are regularly unclothed. Two male-bodied people enter that locker room. One of them is a perfectly harmless transwoman, who is non-op and non-HRT. The other one is a predator who wants to get off on seeing naked women and making them uncomfortable. Let's even assume that anyone who looks like a male gets asked on their way in "Are you a transwoman?".
Do you think that the predator, who is intentionally transgressing women's boundaries, is going to be honest? If he lies, how do we tell that he is lying and that the other person is not?
Secondly... I think your premise is based on a desired narrative. There have now been studies in England, Scotland, Canada, and IIRC California. The percentage of transwomen who are serving time for sexual crimes is significantly higher than that of men in general. I don't recall the exact numbers, but it's something like 5% of men are incarcerated for sexual crimes, and about 40% of transwomen.
Now - let me be very clear here. This does not necessarily mean that transwomen offend at rates higher than men. I think it's far more likely that sexual predators are likely to falsely identify as trans while incarcerated, in a play to get moved to a female prison. But that does bring me right back around to the very heart of the problem: Self-ID.
I don't have a problem with transwomen. There are several that I know personally and rather like. What I have a problem with is Self-ID. That's the problem. The problem is that policies are being written and enacted right now, where any man who says they are trans is granted legal access to female-only spaces... with no oversight, no way to verify that they're not bad actors, and no consideration at all given for the risk and discomfort this places on women. And absolutely zero thought given the the basic concept of consent. It creates an incentive for bad actors to declare themselves trans, because by doing so they are immune to accusations of acting badly when they look at naked women against their will, or when they expose themselves to women without their consent. It legalizes peeping and flashing. And it creates a situation where no prevention is possible... and the only recourse women have is to report an assault after it happens. And when only about 1% or reported sexual assaults ever get convicted, that's pretty much giving a 99% free pass for men to behave badly without consequence.
Self ID has a gigantic gaping loophole that is visible from space.
But women are being told, over and over and over, mostly by men, that we should pretend that we're not aware of that loophole, and we should just pretend that there's no risk... and well... if it turns out down the road that "too many" women get hurt because of this giant loophole... then maybe the menfolk will reconsider it then. But until then, we should just shut up, be nice, and know our places.