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.
4chan in a nutshell