Your logic skills are embarrassing.
He is free to wear whatever he wants off company time. He made his statement by quitting and I support him.
But I see the company’s point. The LGBTWXYZ employee on the next shift will want to wear their rainbow flag. “But Bob can wear his flag!”. Then the Mexican cleaning the rooms will want to wear her Mexican flag pin. And some red blooded American will complain.
The management of the hotel obviously wanted to cut this nonsense off at the knees and focus on more important issues so they just implemented a total ban on pins. Fine and dandy.
The hotel has a huge flag flying right outside. It’s not an American-Anti-American issue. It’s a uniform issue.
An American flag pin is not “just another symbol”. It has special meaning and is appropriate anywhere, anytime, always and forever. Get it?