I don't agree with that at all. He's basically saying, if you don't want your little girls to be around penises, you can't ever take them to a gym, spa, public pool, or any other place with a women's locker room/shower area.
Why should that be a problem? I recall when I was a kid, I was never taken to places where I'd be around naked adults, regardless of gender. If we went swimming at a community pool, we changed at home, before and after. We didn't go to spas.
I do recall when I went from 6th grade to 7th grade, which was the point when boys would start dressing out for P.E. class and taking showers after class. That was mandatory, although at some point a few years later, it was made optional. Now, as I understand it, it's unheard of at middle and high schools these days. I hear some schools just use the shower areas to store equipment, that they're not functional anymore. I don't know if it's the case in all schools, although I get the impression that it's not how it used to be.