To begin, hat check stations have all but disappeared along with hat racks or even clothing hooks in restaurants and other semi-public places.
Second, you never want to sit anywhere your hat is out of immediate view. I know not why, but "things happen" to hats, especially expensive hats.
Three, the etiquette is all over the map. Watch old clips of Candid Camera and you will see, for example, men did NOT take off their hats in the Automat. (Remember the Automat?)
I have been admonished to remove my brimmed hat in a room filled with men wearing baseball caps. Apparently brimmed hat wearers are held to a higher standard of courtesy.
If a man aspires to wear a brimmed or fedora style hat in modern society he will need to be prepared to brave the slings and arrows of outrageous approbation of one sort or other everywhere he goes.
Overall, public opinion has never really bothered me.
Best regards,
Excellent post.