I think a lot of it has to do with the delivery. Tony Barrand told how Marie Lloyd, the English music hall star, was brought up on charges singing indecent songs or somesuch. Her defense was to sing one of her hit songs, "Daddy Wouldn't Buy Me A Bow-Wow" "straight", with no nods, winks, etc. and then to follow it with a song then very popular in respectable circles (like judges and their wives): "Meet Me at the Garden Gate" (or something similar; I'm doing this from memory) This time, of course, she threw in every innuendo she could, emphasis on certain words, etc. How could she be brought up on charges for the former song when no one was being hauled in for singing the latter? She was found not guilty.
One of the finest bawdy renditions of any song I've ever heard was a late-night rendition of the hymn "Rock of Ages". Neither the words nor the tune were changed.
Another thought comes to mind. At a concert once, Peter Bellamy told of an elderly gentleman who had a song called "Cock-a-Doodle-Do" that he sang at annual family gatherings. It was full of double entendre, but this was never acknowledged by either singer or listeners. Then apparently some of the younger set began sniggering at *those* parts of the song, etc., and he stopped singing it, because the unacknowledged presentation was humorous, and the acknowledged one was vulgar.