In the early 20th Century men switched from straw hats to felt ones on September 15th. If a man ignored this edict hooligans were free to smash his hat to bits.
The article above describes a hat smashing incident in 1922. A group of 1000 from the notorious Five Points neighbourhood prowled the streets of New York City, beating men who refused to remove their straw hats.
Via Dr. Caligari's Cabinet