I think I've blogged about the photos showing men in the 1920's-1950s wearing hats. It seemed to be universal, not an indicator of class.
In an attempt to be fair, I want to link to this tweet, with a photo showing 1920's women wore hats as well. Apparently the gender difference was that women wore hats everywhere, but men only outdoors?
Aug 7, 1920 - William Hays, Chairman of the Republican National Committee, and a delegation of Connecticut suffragists at Republican National Headquarters in New York City #100yearsago pic.twitter.com/FTAoinFuKY
— Patrick Chovanec (@prchovanec) August 8, 2020