Hats!

[Sumpter250]

But was going out without a hat considered taboo, or was it just considered foolish?

I can't remember!
I think wearing a hat was simply considered "the proper thing to do". I do remember wearing a hat, whenever I wore a suit, and I do remember my father wearing a hat most of the time, at least into the early sixties.

Hat brims can be "punched out" with a leather punch, check your local craft/fabric stores for the punch sets.
I've also used the punches on up to .040" styrene, to make numbers of disks for several modeling applications.
.005" styrene can be used for brims. It would take a bit of practice, but a hot soldering iron could be used to "form" the brims. (or maybe that's "deform")