My Red Hunting Hat

Literally, a red hunting hat is used to distinguish yourself from the deer so that the other hunters won't mistake and shoot you, well let's move into the metaphorical meaning.
Holden finds pride in his wearing his hat, it's something that has become a part of who he is, feeling like some sort of hunter among the phonies or to let the 'real' people know he's there or maybe looking for those who don't "fake" their way around life. I feel that he also uses it when he's had a shift in emotions or thoughts, such as when he playfully held Stradlater in a half-nelson or when he felt nervous about Stradlater going out with Jane Gallagher. It's almost like a 'tell', an action (even a minuscule one) that people can use to know that you're lying.

Another interpretation to the hunting hat is an item that brings Holden some level of safety, maybe feeling that he has more power than he really does. In this case, everyone might have their own hunting hat, some charm, item or even thought that makes them feel in control.

I can't say that I'm too sure what my own red hunting hat is maybe it's the smile you use to distinguish yourself to people, to let them know that you're a friend or a frown to let people know 'I'm not in the mood to deal with you". It's not my best interpretation so enjoy this hat instead.