I grew up post-Kennedy, so hat etiquette was not something I was particularly raised with. At various times during my school days (including college), I wore a flat cap, a wide-brimmed "Godfather" style fedora, and assorted ball caps. Once I started doing Steampunk costuming, I rapidly acquired a top hat, a bowler, a flat-crowned "Gambler" style cowboy hat, a pith helmet, and assorted fezzed, tarbooshes, and glengarry-style hats. It's been interesting watching my own reactions change over time - as part of a costume, it's not uncommon for hats to remain on heads when inside at a convention, but at dinner (for example, on the Steampunk Cruise), hats were removed about half the time (and usually by the same people). I'm finding myself wearing hats more often now (a Panama in the summer, a new Fedora now that it's cold out), and I almost instinctively take my hat off when entering a building, though if I'm headed for an office where I know there's a hat rack and I'm wearing a heavy coat, I may leave them both on until I can remove both and hang them up.
Things change over time - and as more people return to wearing hats, I'm sure that more rules will reappear as society demands.