GUEST said "I'd suggest either giving a brief intro explaining that the song contains the [currently offensive] language and attitudes of a previous era or simply avoiding the song altogether."

I think an awful lot of very good songs from earlier eras would be lost if everyone followed that rule.   Many music programs are not meant as history lessons per se and don't work well with extended explanatory introductions to songs. Plus, sometimes there are people in the audience who would, perhaps rightly, still be very offended by the use of some words, even if you've explained the context.    I think if altering the words can minimize such offense without really changing the character of a song, why not modify them as needed? But if 'sanitizing' them (e.g., "... You're a bunch of stinkers all, gosh darn your eyes") really messes up a song, don't sing that song for that audience.

I don't think there's a hard and fast rule that applies for all songs and situations.