"the sign of familiarity of his wearing no hat"

Until around the 1960s, hats were de rigeur for men. Not only did they serve a practical function in protecting their wearers from the elements, they were also bound into patterns of social etiquette: with a hat, respect for customs could be expressed. It was doffed as a mark of reverence for a lady or a social superior, removed before entering a church, and held to the heart during the national anthem.  Peter Quint’s bare-headedness so offends the governess because it demonstrates an indifference towards such proprieties.

Hats began to fall out of fashion with the rise of the automobile: when one no longer travelled on foot, there was no need to protect oneself from the vagaries of the weather. The shift towards comfort and practicality in dress and away from formality also played a role.