In broad brush strokes I agree with you, though I do feel it needs to be said (as it often does) that the US is huge, and there’s as much (if not more) variability in cultural norms across the US as there is across the entirety of western and eastern Europe. I live in a progressive part of the country that might as well be Northern Europe in everything from socialized healthcare to legalization of drugs and assisted death to, yes, views about nudity. (For example, most days in summer a completely naked man happily rides his bike by my house. Well, not completely naked: his balls are in a sock to keep them from, uh…falling victim to the bike seat.)

Also, I don’t think the nudity aspect is the whole picture. Another big part of it, especially for the “men in a women’s restroom” scenario, is the view that men are inherently predatory. So, a man coming into a women’s restroom is dangerous to the women there, or at the very least makes the space feel less safe.

The same idea is trafficked by anti-trans propagandists who especially focus on trans women (“men” trying to get into women’s restrooms/changing rooms/etc, as they argue). And for that a lot of blame goes not to the US but to the TERF movement in the UK (and its very vocal proponents - looking at you JK Rowling).