Simply put, bollocks.
Please cite me one genuine case where a man "has put on a dress" to get into women-only spaces in order to assault women, because I really think you can't do so. Even if you were able to, it would be far outweighed by the cases of men just going into women only spaces and assaulting women, and this line of argument makes this vastly more likely, not less likely, because, and I'll state this again, and this time spell this out in block capitals so it can grab the attention of your rather dim mind: REQUIRING PEOPLE TO USE THE TOILET OF THEIR "BIRTH GENDER" AFTER TRANSITIONING MEANS THAT CIS-GENDERED MEN (THE ONES MOST LIKELY TO ASSAULT CIS-GENDERED WOMEN) CAN SAY "I AM A TRANS MAN, SO I HAVE TO USE THIS TOILET" AND WALK INTO A WOMEN'S TOILET IN ORDER TO ASSAULT A WOMAN.
Now, the whole argument around toilets in regard to "protecting women" is utterly specious, because not only do men already attack women in women's toilets (there isn't some sort of magical force-field that stops them going in there), men also attack women in lots of places that aren't toilets. At work, at home, on public transport, OUTSIDE TOILETS, in bars, in restaurants, pretty much everywhere, and turning the eye of scrutiny on the already marginalised trans community does absolutely fuck all to address the real, and ever-present problem of toxic masculinity and "rape culture". The argument boils down to "if only it wasn't allowed, it wouldn't happen," which is obvious bollocks as evidenced by the existence of murder trials. The deceptive language of dressing up trans people as "part of the problem" is transphobic, whether or not you have been pulled into the argument through ignorance, or have wilfully gone down that line of reasoning with full knowledge of the implications, like JK Rowling has. It is faulty logic, based on biased reasoning, which has "trans people are a threat" as its ab initio condition. "Fear those people because they are different to you, and therefore should have fewer rights". That, my good sir, is fascism.
FWIW, I have friends in the trans community, both trans men and trans women. None of them corresponds to the sort of crude caricature of "sex offender by default" that "gender critical activists" like to implicitly portray.