Despite what the law might say, there’s no evidence whatsoever that letting trans people use their preferred bathroom causes any “injury or harm” to cis people.
To the contrary, there is evidence that restricting bathroom access is harmful to trans people - and cis people too, like Jay, a cis woman who was harassed in a bathroom after being mistaken for a trans person.
Even if they use the “right” restroom trans people are in danger of being harassed all the same if they pass too well: https://www.advocate.com/news/2022/7/12/trans-man-brutally-assaulted-using-womens-restroom-campground
Damned if you do, and damned if you don’t. The point of laws like this isn’t to protect cis women and girls, it’s just to cause as much suffering as possible, because that’s all Republicans care about.
Also there is evidence that it is harmful to cis people. Especially cis women who might be queer or straight or gender nonconforming or not. These fuckwads always forget trans men exist and just harass women more with this shit. They don’t give a fuck off you’re trans or not, it’s about control. And their especially interested in controlling women.
It’s also directly tied to fascism. Eco points to Machismo in point 12 of Ur-Fascism. “[Fascists hold] both disdain for women and intolerance and condemnation of nonstandard sexual habits, from chastity to homosexuality.” Meaning it’s not just women, trans women, gay men, people outside of traditional 1940s gender roles, but it also includes straight, cis men who just don’t seem to be straight and cis enough.
Despite what the law might say, there’s no evidence whatsoever that letting trans people use their preferred bathroom causes any “injury or harm” to cis people.
Can confirm: Having shared many a bathroom with trans folks and I have managed to survive unharmed. Who would have thunk?