The song is a humorous criticism of musicians that put their political views into their music. It tells the story of a folk song group that is "long on musical ability", but ultimately breaks up due to political differences. At the end of the song, a warning is given not to mix politics with one's music.
The punch line to the joke is that "the guy in the rear", is less easily labeled: he is a Methodist and he burned his driver's license (rather than his draft card), etc. Indeed, the song closes by stating that he got drafted.