Almost every man wore a hat until the 1960s. There's a bunch of weird culture about this.

https://en.wikipedia.org/wiki/Straw_Hat_Riot for instance

There's lots of pictures of the event if you search

I wear a hat outside. It makes walking in the Seattle rain quite pleasant, as my glasses don't fog up and the water doesn't go down the back of my neck. When sunny, I don't need to apply sunscreen, and the glare from the top of my head does not cause car crashes.

As a bonus, I can imagine myself as Clint Eastwood.

Men wearing hats is still quite common today. But the style has changed to baseball caps and similar forms. Most of those "dress codes" usually also have a more practical origin. So it's less of a code, and more a practical benefit.

If you are interested in this topic, especially from the US perspective, I recommend this book: https://www.alibris.com/Hatless-Jack-The-President-the-Fedor... . There was apparently significant social pressure for all men to wear hats until the mid C 20th.

Was this some sort of dress code?

Yes

People were spending much more time outside and the roads were much more dusty. You need a hat to keep yourself from the sun and the dust. Cars made them obsolete.