That was also back when every place had a hat rack, too. You supposed to carry it around with you now?
It was customary then, not for ceremony, but because your hat was FILTHY.
I always thought a tip of the hat was to show that you didn't have anything hidden under there? Like a small pistola. Today, at banks and such I suspect it is because the hat brim probably covers your face and any up high cameras most likely wouldn't get a good shot of you for the evening news.
Generally, we take our hats off indoors although I suspect this is becoming less common and expected, due to different reasons. I take my hat off at the school. I would go cash a check or withdrawal money if I was in and out quick, with my ball cap on, but I would take it off if I was sitting down to sign papers for a loan or such.
I do lots of sports banquets and appreciation dinners and things like that. Out of 500 people, there will always be a few guys wearing ball caps eating a meal, mixed in with some who thought a suit and tie was appropriate wear. We don't have a whole lot of cowboy hat wearing folks around here.