"Also, gender segregated toilets that are located in convenient, safe locations at school can protect girls from violence and assault. Women and girls are often vulnerable to harassment or violence when they must use shared toilets or are forced to go to the bathroom outside. In one survey of schoolgirls in South Africa, for example, more than 30% reported having been raped at school; often these incidences occurred in school toilets that were either shared or in unsafe, isolated locations. Such violence is a major deterrent to school attendance, not to mention a girl’s self-esteem and desire to learn."
There's a lot wrong with that, so it's hard to even know where to begin.
First, they're lumping together bad behavior in shared restrooms with bad behavior in "unsafe, isolated locations". The fact that unsafe, isolated locations even exist is solid evidence of inadequate staffing, so we can start from the assumption that these schools aren't otherwise safe to begin with. No bathroom policy will change those, and lumping them together disguises the signal that they're complaining about (women being abused in shared restrooms) with a giant pile of noise.
Second, it goes without saying that in a school situation, a shared restroom has to be monitored. Even if you didn't have people getting raped, you'd still have people sneaking in to have sex, smoke, drink, do drugs, and so on. The real problem is not the shared nature of the restroom, but rather the lack of monitoring.
Also, you can bet that there are incidents in those same schools where people have been beaten up in the restroom, but nobody is complaining about those, because that doesn't give them an easily defined group of people to hate. Yet the same fix — proper staff supervision — would fix both problems, whereas a non-shared restroom only fixes one of those problems, and potentially doubles the number of staff needed to fix the other one.
Finally, the "or are forced to go to the bathroom outside" part is the point where most rational people would simply write off the entire argument as nonsensical in the context of any rational discussion of the United States unless you go back a hundred years or more.
If you lump in enough unrelated signals, you can absolutely create something that *looks* like a signal. I can do that, too. In Georgia, Mississippi, Texas, and San Francisco, people with hunting rifles kill [insert number of people] every year. Therefore, we need to ban hunting rifles in San Francisco. See how absurd that sounds when it is used to defend something the left would be more likely to support? It sounds just as stupid coming from the right.