Prior to the mid 1960s and Vatican II, Roman Catholic practice was for males never to wear any kind of head covering in church, while females were absolutely required to have something, anything, on top of their heads. Like Joe said: "(or, in emergency, Kleenex)."

I don't remember the mantilla as coming into style with Jackie Kennedy. My recollection is that it was already established as an alternative to a real hat for churchgoing Catholic women. A mantilla was (is?) a fairly flimsy bit of lace you could drop onto your skull in order to comply with the headwear rule. I'm sure there were specific ways to folk, drape, and position it for maximum fashion conformity.

I feel pretty sure that those gender-specific headwear-in-church rules gdate back for centuries, and were probably in force throughout Christendom even before the Protestant Reformation. Now, only a half-century after the rules were relaxed by the last remaining institution to take these rules seriously, the whole deal seems to be very largely forgotten.

Now, traditional Jewish practice is to require men to cover, not uncover, their heads in the sanctuary. I have no idea what the rule might be for women. Anybody? Anybody?