Lots of religions have their own hats. The jews've got spodiks, shtreimels, and yarmulkes; Muslims have taqiyahs and turbans; various Christian denominations have their assortment of hats: mitres, wideawake hats, kolpaks, birettas, galeros, et cetera; people who worship science have oxford caps, pastafarians have spaghetti colanders; and the traditional hat of Gnostics is perhaps the easiest of all religious headgear to craft: the aluminium foil pickelhaube
The aluminium foil pickelhaube thing is mostly a joke but I have worn a tin foil hat before and it does seem to have an effect