Well, so flags were pre approved? I guess thats because if you go through the trouble of waving a flag in public it can mean only one thing. A flag has only one purpose. Its purpose is to show an affiliation with or support of something..etc ..along those lines. Unlike a hat, a flag is not an article of clothing which can serve multiple purposes. When have you ever heard of going to an event and needing to have a hat pre-approved?
Why should anyone have to get a hat pre-approved? I might wear a Detroit Lions hat simply because I like the shape and color, I might wear it becaus esomeone close to me gave it to me as a gift.. I dont have to be a fan of the Detroit Lions in any way ..and whos business of anyone is it to ask the reason why I am wearing that hat... there can be multiple reasons. It's also unfair to do the same with a red hat that says MAGA on it.
I realize its not you who is making these rules , but this is very wrong in American society.