Baseball caps were originally made of straw.

Straw was used to make the first baseball caps in the US. The first
official baseball team uniform was implemented in 1849 by the New York
Knickerbockers and consisted of wool pants, flannel shirts, and straw hats.
This style was mainly worn until 1860, when the Brooklyn Excelsiors adopted
a merino wool cap with a soft rounded top and a bill that eventually became
the modern baseball hat. The first major league team to adorn their
official hat with an image of their team mascot was the Detroit Tigers, who
donned caps with tiger images on them starting in 1901.