You can wear hats there, Butt if there are specific and special events that day, most of the time they will ask you to remove your hat if there is a sport logo on it or any type of advertising
Yes you can but not recommend
it all depends on the venue you should call and ask for whatever your Venue is. I've been to a couple of shows where they were filming for a national television network. And they did not allow any endorsements for any thing drinks sports teams Etc
Seen ppl wear hats yeah
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