Come to think of it, I do have a coworker who wears a hat/cap indoors. She's young and cute and has a sort of artistic fashion sense, and wears a small soft beret at times. Looks nice on her and I don't think anyone would find it offensive. And come to think of it, some of the younger computer support geeks wear caps indoors.
In general I think hats or caps are a bit different from covering up "boobs and butt", more like an inoffensive fashion choice.