Hector Ramirez sort of knows, from watching old movies, that men are supposed to take off their hats when indoors. But the 19-year-old Brown University student wears fedoras in class—with jeans—anyway.

"If I'm wearing a hat and it's part of my look, I don't think I should have to take it off," he says. On a recent trip to New York, an usher at a church had to remind him to take off his fedora. "I was wearing it all day and I guess I kind of just forgot I had it on."

Inspired...