In reply to:

I've always wondered how the theatrical term "going blue" originated to describe the use of profanity onstage.

To make the air blue: a vigorous and plentiful use of cuss words. According to Charles Funk, the origination of the meaning is a matter of guesswork, but he traces the blue/obscene association back through associations with blue devils (1616) and the plague (1742). Joseph Roppolo, of Tulane University, associates the devil/blue meaning with blue blazes = hell, and hence to obscene.

On the other hand, I recall reading someone's explanation that the smokey atmosphere of the places in which obscene entertainment was presented lead to the blue association.