GW Rule #26

In pulling off your hat to persons of distinction, as noblemen, justices, churchmen &c make a reverence, bowing more or less according to the custom of the better bred, and quality of the person.  Amongst your equals expect not always that they should begin with you first, but to pull off the hat when there is no need is affectation, in the manner of saluting and re-saluting in words keep to the most usual custom.

PEEVES

Taking off your hat is a sign of respect, especially to the elderly. It’s not necessary to your pals.

MADAMA

An honorable person takes the time to show respect to those who came before them, especially those who have been of service and gave their lives: military, spiritual leaders, police, medicals professionals, and so on.

SANDRA

Hats also hide most of your face.  When you remove your hat, your feelings are shown.