Extra points if the word implies that the person in question is pious.
"puritanical" or “straight-laced”
“prig” or “prudish” may be taken as pejorative; if that is what you intend. (Although your own term “pious” may work nicely.) - http://thesaurus.com/browse/prudish
Also – “stuffy”, or “prissy”
To someone’s face you might use “moderate”, “reserved”, or even “appropriate”, as I think most people believe appropriate language is simply language with no cussing or off-color remarks, used for large audiences and moderate minds.
Also – sensible, restrained, measured
Or - goody two-shoes! - http://thesaurus.com/browse/goody+two-shoes
Or perhaps “Ned Flanders”...
If I were you, I would use prude, never mind the context.