Check out this video, in which you will see men wearing hats while doing construction, with no foul language, long sleeves, pants, and I would guess many are non-Catholic.
I recall my grandfather saying all men wore hats until the bad example of President Kennedy (Catholic), who showed up to a baseball game with bare hear, and started a deleterious trend.
I wonder if a haberdashery would have any chance of making ends meet?
Anyway, a glance back to a "cleaner" time: