I can recall visiting a friend who was playing the organ at St Pat's Cathedral (Melbourne) about 40 years ago. In the organ loft was a music book with the title "Sacred and Profane" or words to that effect. With only a secular knowledge of the use of the word "profane" I enquired of him why such music would be allowed in a catholic cathedral. I can't remember his exact words but the sense of his reply was very much along the lines that Joe Offer has so eloquently explained, above.

Ta muchly, Rowan