I don't find that funny, any more than Jewish jokes, Liza and Rastus jokes, or Irish jokes.

Who said folkies had no sense of humour? The Fast Show parody is done by people with a genuine love of the stuff, and a despair for the creeping idiocy that would ever take offence at such an accurate & affectionate send up. And in no way shape or form is it racist; folk music being a hobbyist concern of but a tiny minority of the 70 million (or so) citizens currently resident in the British Isles and not a manifestation of the ethnicity of same.