Whilst I applaud your appeal to moderation, I am laughing whilst clapping that this should come from somebody who frequently associates trans women with sexual predators.
No, I frequently associate sexual predators with pretending to be transwomen.
Can they? Largely not. The next step is to consider why not.
I would submit that there is a noisy cohort of people who are sending death and rape threats to anyone who decides that maybe a discussion needs to be had about women's rights to safe spaces, to play sport fairly etc, as well as organising protests to shut down anyone who offers an alternative point of view or asks for a discussion.
The reason that "Let Women Speak" exists is because of the above. The extremist views of LWS are pretty much outlined here;-
https://committees.parliament.uk/writtenevidence/17158/pdf/
Spoiler: They don't seem to be that extreme.
Similarly JK Rowling is vilified and called a transphobe, send death threats, rape threats, threats of violence etc for supporting the notion that some women are concerned about law changes that might affect their safety. Transwomen like India Willoughby like to get on their high horse about being "deadnamed" despite horrific posts threatening to kidnap or attack people such as JK Rowling.
It's a simple fact of life. If you ban someone from performing, more people will want to see that person performing. The more that the purse clutching "transwomen will die if this person performs" brigade try to shut people down, the more vocal those people will get and the more the issue will escalate. Very few of the people who the issues are actually about - i.e. transgender people with genuine dysphoria issues - will benefit or get involved, and has been mentioned before, will probably see an increase in hate attacks.
I'd suggest that it isn't LWS fanning the flames it's the pro-trans extremists egged on by the press and by organisations wanting to be oversensitive, terrified that saying the wrong thing will affect sales. See Hogwarts Legacy and the Gaming Press for more details.