Not wearing one in public i.e amongst other people, or worse flagrantly not doing so, is just being a dick. Simple. Politicians not leading by example - whether Republican, Democrat or Independent - is just being a dick. I carry one with me. I don't wear it walking down the street when I can comfortably distance from other people but I will put it on well before entering a store or public place such as any building or queuing even if outside.
Political statement. Fashion statement. Whatever. People have been doing that with T shirts ever since they were invented. No surprises there. Either way, wearing one or not around others becomes a matter of whether you want to be courteous and respectful or just be a dick - whether standing before a nation or in line at a bus stop. Better to bias towards the former, and to set an example, than the latter.
Forget about the hat for a moment - although it may be difficult not to - what sort of image does this man portray before others? I couldn't care if he were wearing a Trump cap, a Biden cap or no cap, the guy is still a dick.