I don't care what people guess my politics to be based on that. It keeps my ears warm enough to sweat when it's like -25*F outside.. sometimes a cigar is just a cigar and sometimes hats are just for warmth
My son has one like that as well. We weren't thinking about politics when we bought it, but rather about his health.
I agree with the rest of your post as well. A beret is a beret, a cowboy hat is a cowboy hat, a fedora is a fedora, and most of the time people wear hats just to keep warm, or to keep the sun out of their eyes when they're swinging a bat or pitching a ball or riding a horse. Or, in some cases, to cover up a bald spot. I don't recall ever making assumptions about anyone's politics based on their hats.
Certain sections of the right have adopted certain styles of the left (surprise, surprise); meanwhile, some with right-wing views may still be "hip" style-wise--think of a son of Macomb who nonetheless likes EDM and joggers. Of course, I, like many people, like to ascribe worldviews to people I see on the street, and maybe they're mostly right, but they're certainly never "all right".
1. Of course we don't choose hats based on our politics! (As I said in the OP: not counting hats with explicit political messages on them, such as the MAGA cap.) Rather, I think our choice of hats and our politics are somewhat derived from a common source: some mix of tribal identity, personality traits, and other stuff, maybe even including something as basic as our testosterone levels.
2. We're talking about stereotypes here, people. They're not accurate 100% of the time, and in some cases maybe not even 50% of the time, but they are usually accurate enough of the time that our brains can use them to allow us to make tough calls quickly; tough calls such as gathering metadata about strangers at a distance. Back on the African Savannah we needed to figure out whether the hominid on the other side of the watering hole was a friend or foe, and if we weren't close enough to talk or read facial expressions then we'd probably end up judging based on whether his jewelry and tattoos marked him as part of a friendly tribe.
3. Obviously if a guy in a cowboy hat starts saying liberal things then we know he does not fit the stereotype about guys in cowboy hats. We shouldn't tell him "You can't say that, you're wearing a cowboy hat!" We have to remember that most men's hats are functional and don't
necessarily convey a political affiliation.
4. Testing out stereotypes is fun! I'm personally a huge fan of games like this and I delight in how accurate stereotypes so often are. It's exciting to find the little hidden keystones that hold together lots of different variables that might otherwise seem random, and in my opinion it speaks to the marvelous and splendid orderliness of our universe. (Which we should enjoy while it lasts because entropy.)