You sweated into the hat, the water evaporated and the salt remained. Salt sucks water right out of the air in a humid environment. Wash the hat and it will stop getting moist ... temporarily. I learned this little gem when tanning salted deer hides; stored in an open garage doorway near falling rain they got wet even though the rain never actually touched them. Amazing how science works.
I thought about washing it, but if the inside of the bill is cardboard instead of plastic, it'll go all funky.