Since there are no "rules" anymore, I look around and put my hat any place that is safe lol . I'll put it in the pew next to me in church, on my knee, on top of the pile of coats, on the edge of the restaurant table. If there is no place to safely set my hat, I'll keep it on my head, and if someone doesn't like it, that's their problem!!!
There were never any rules, only customs and good manners. Those are still in place. Moving the "problem" to someone else doesn't change anything. It is still rude to eat with a hat on your head. Nobody is keeping you from being rude. It is a choice you make. In my case, if there is nowhere to put my hat, I put it on my lap.