Muslim men often cover their heads too, particularly when praying in mosques. It seems to be entirely a personal matter (in Turkey, anyway). It's quite common for men to use small knitted skullcaps - smaller and stretchier than the typical Jewish yarmulke, and never held on with a pin - I think the idea is that the most devoted mosque-goers have little enough hair left that a pin would be pointless, so they grip by friction. Also they fit easily in your pocket. I carry one in Turkey to wear when it might help to fit in.

Jeremy Seal's "A Fez of the Heart" is one of the oddest travel books I've read. He goes round Turkey tracing the history of state intervention in men's headgear. As with women's head coverings, a frequent theme is that the worst intolerance (up to the point of massacre) has more often been on the part of the secularists. I can see on the web that there is a Turkish dance-song "The Man Who Passes By Selling Caps" (relating to Ataturk's forcible imposition of the Western flat cap) but haven't yet managed to find the song itself.