There aren't hard and fast rules about these kinds of things - it's like jokes. At one extreme you get people who are telling jokes about their own community/nationality/whatver in away that is affirming its strengths and its humour. And there are lots of in-betweens. But they all might be telling the same joke, but with a different meaning. And the same goes for songs.

The first thing that matters is the intention within the person telling the joke or singing the song; and the second is the likely way that the particular audience is going to take it. But of course in these days of canned music and so forth the audience can be anyone, and the discretion that good performers alwys have with a live audience is undercut.

"Offending" isn't the right word. "Insulting", and "hurting" are better ones. And more important, licensing prejudice.