The argument: If you let trans women use public restrooms that match their gender identity then men will claim to be trans women so they can ogle, harass and/or sexually assault women.
The reality: Harassment, sexual assault and invasion of privacy is already illegal, and incidents of harassment didn’t increase in places that passed non-discrimination laws allowing trans people to use bathroom matching their gender.
From a logical perspective the whole safety argument is dumb: as comedian Raanan Hershberg put it, “that means you you believe that there are guys out there going ‘Man, I’d love to go into a woman’s bathroom and abduct and murder someone… but unfortunately I’m not allowed in there.'” But it’s powerful emotionally, and fear of sexual predators has been used time and again to convince an otherwise tolerant public to support discrimination, from using fear of black men attacking white women to support racially segregated bathrooms in the Jim Crow South to using fear of unisex bathrooms to tank the Equal Rights Amendment in the 1970s.
Ironically bathroom bans embolden random strangers to insist that women provide “proof” of their sex for the temerity of using a public restroom. The also require trans men to use women’s public restrooms (and vice versa), which needless to say will not make anyone feel more secure. But as amusing as that image might be (until the poor guy gets pepper sprayed just for following the law) the bans mostly just encourage trans people to avoid public restrooms (and public spaces) whenever possible, and that’s probably the real goal. And as with sports, cis women who don’t look feminine enough are are also being targetted [archive].
One thing that makes me optimistic is how much of an improvement the design of modern unisex restrooms is over what I grew up with. The traditional bathroom stall design (especially in the US) lacks privacy and make people feel uncomfortable regardless of gender issues, so it’s understandable that sense of vulnerability is exacerbated when you add the idea of strangers who are trans also being there. Modern gender-neutral bathrooms, changing rooms and showers are designed with with single stalls around a semi-public common area for hand washing and the like, which is not only more private for everyone but also solves the question of which restroom non-binary people should use (not to mention making shorter lines for the women’s restroom).
How it’s being weaponized: Nineteen states have passed bathroom ban that apply at least to K-12 schools, with eleven extending to at least some government-owned buildings and properties. The Trump administration is threatening to withhold federal funding from K-12 schools that don’t make similar bans of their own (even if doing so goes against state law), and is also reportedly targeting K-12 schools that have installed gender-neutral bathrooms for violations of anti-discrimination laws.