In American culture, why is a woman going topless fairly acceptable as long as her nipples aren't showing?

[Mark]

Because people like to push boundaries. It's also why full dorsal nudity is common on TV, but full frontal nudity isn't.

What's even funnier is this behaviour has gone on for hundreds of years, not just in the US. Women in England in the 1700s used to wear kind of thin dresses, wet, so you could more or less see everything, but they could fall back on "I'm covered!" if someone objected to it.