Emily Post, in Etiquette (1922):
People do not greet each other in church, except at a wedding. At weddings people do speak to friends sitting near them, but in a low tone of voice. It would be shocking to enter a church and hear a babel of voices! Ordinarily in church if a friend happens to catch your eye, you smile, but never actually bow. If you go to a church not your own and a stranger offers you a seat in her pew, you should, on leaving, turn to her and say: ‘Thank you.’ But you do not greet anyone until you are out on the church steps, when you naturally speak to your friends. ‘Hello’ should not be said on this occasion because it is too ‘familiar’ for the solemnity of church surroundings.
One might still greet people, I think, in the narthex afore the worship space, unless there was no well-defined narthex. As a man of high-church sensibilities – and it seems Mrs Post shares my sentiments – I do rather dislike talking in church, though it seems only right to speak when spoken to, however quietly. In a low-church parish it can be harder to know what to do, when everyone talks in church. I suppose one can move quietly into the pew and be in prayer until the service starts.