This whole topic is interesting to me - hats, and other clothes as well. I read up further that several people had heartburn about folks wearing shorts etc and how some things are "grownup" or inappropriate. My take is this - it doesn't matter what you wear as long as you can pull it off. What I mean, I see so many people "dressing up" that look like they are trying way too hard, and it is unnatural and very noticeable. One guy can wear a fedora and look like he was born with it on, and many others just look goofy. I look really natural in a ball cap, my drummer just looks funny with one on. When I see jeans on people doing a show in hot weather it looks goofy as hell unless they are country and got their boots and cowboy hats on. All black with jeans on a hot, sunny outdoor stage.....lol. I want to wear one of those English driver caps, but I look stupid in one, whereas some people just look awesome.
I guess my main point is be true to who you are and dress that part, don't try to pull off something that doesn't work at all or isn't really you as it looks that way. First and foremost, play the music and play it well, look and smile at the audience - my favorite bands are the ones that can do that and look like they just walked in off the street in "normal" clothes and style and appropriate for the weather. I was a teenager in the 80's and the goofy clothes worn by bands then tainted me on style for musicians, they were becoming more about flashy looks than music - I think they spent more time at the mall than writing lyrics.
Of course, this is obviously dependent on the show - no shorts at a fancy wedding and no floral shirts at a funeral.
With all that drivel out of the way - I like to wear ball caps and currently sport a Patagonia model - brings the thump!!