I just finished reading Ursula K. Le Guin's book Voices. The priests in this book all wore red hats. They were called the Red Hats.
Coincidentally, I have been seeing a lot of red hats in catholic news these days.
The Red Hats in Le Guin's book were not kind men. I am not making any kind of comparison to the real cardinals wearing red hats and working together to pick a new pope in the Sistine Chapel.
Out of curiosity I did a quick search of catholic hats. I was surprised to find so many official hat names.
movingforwardslowly 