In a few parts of the US, hats are used as a gang insignia, and are part of the whole infantile gang bit about "showing colo(u)rs." Since prohibiting the display of "colours" (and any other gang insignia) often results in "problems" with the gangs, a few places resort to prohibiting "items of clothing that might be used as gang insignia" for all patrons. A stepson was occasionally refused admittance to a few places because of his "dew-rag"¹, which he wore to keep the drippings out of his eyes while working as a framing carpenter, but is an "item of clothing" favored by some (especially biker) gangs.

¹ dew-rag, sometimes do-rag, (occasionally called an "Aunt Jemima" esp. by ethnic gang members,) is simply a handkerchief (large) tied on the head to keep the hair (and sweat) in place. The term is most often used when the "tail" of the 'chief covers the top of the hair, but sometimes is applied when it's rolled into a band across the forehead above the eyes.

While I don't know that this would be a likely reason for prohibiting hats of more general kind, especially outside a few of our infested US cities, it's a possibility to be considered almost anywhere.

Prohibiting all headwear could be the cop-out alternative to confronting someone about possible "associations."

Other reasons speculated probably are equally likely.

John