Except it's not an USA thing. Here in Europe showing nipples in a public place is also considered nudity and generally frowned upon. It's a cultural thing, no need to attribute ideology to it. And the culture is shifting - just a century ago it was considered not modest if you wore shorts or short skirts, or two-piece swimsuits, now it's normal and accepted.
It's a USA thing. Where I'm from in the nordics they have bus advertisements with nipples on them. There is no issue with breastfeeding or semi-translucent clothing in most of Europe.
Look at european cinema and TV, there is a lot of nudity.
The fact that women have to censor photos of their nipples on Instagram is outrageous to me.