This argument is just an embarrassment. Like public bathrooms are the last bastion of safety for scared women left in the US? No, just no. I'm an anti-feminist in a lot of respects, but this is across the line for even me.
I'm /way/ more afraid of the smell invading my brain with a tape worm, than I am of some rapist hanging out in there (and yea, I know worms don't ride on smells, that's exactly how ridiculous this argument is to me.) I have a list of single bathrooms that are cleaned on a regular basis on my phone, even those toilets are for emergency use only, but it's called taking responsibility for myself, and my /personal/ preferences (which happens to be an extreme dislike of all public bathrooms)
This is not discrimination, it's not a safety issue, it's not a right or an entitlement. It is a case of making a personal choice about what bathrooms you're willing to use - or none at all. It's not hard to avoid public bathrooms entirely, I cannot recall when I last used one (though granted I tend to only be out n about for my weekend shopping trips) still I have zero difficulty waiting until I get home so I don't have to worry about what state the bathroom is in. 10-12 hour shopping runs, no problem at all waiting until I get home. What state the bathroom is in, is no different than if a place has transgender bathrooms or not, these women need to make a personal choice about using them; and if they decide /not/ to, then they need to be personally responsible for planning around that idea - be that going to another shop that has a single person toilet, or holding it until they get home. Personal responsibility.