In the late 1970s, some members of the punk subculture on the West Coast of the United States began to use Nazi symbolism for shock effect, and others adopted neo-Nazism in earnest. Dead Kennedys were one of the bands that became popular among the neo-Nazi punk movement when they were misinterpreted as right-wing polemicists. Their gigs began to attract a significant audience of neo-Nazi skinheads, perhaps thrown off by the title of the song "California Über Alles". The Dead Kennedys were actually quite the opposite, loudly opposed to the fascist tendencies that the neo-Nazi movement espoused. Angry at what the Nazi punk movement was about (believing it was not true punk), the group wrote "Nazi Punks Fuck Off" as a response to the boneheads invading their shows, telling them that they wanted nothing to do with neo-Nazism and that by using Nazi symbols and imagery, they were going against the very subculture they claimed to be a part of (as shown in the lyric "We ain't trying to be the police/If you ape the cops, it ain't anarchy").
The single included a free armband with a crossed-out swastika. The design was later adapted both as the Dead Kennedys' logo and as a symbol for the anti-racist punk movement.
Manchester engineer Martin Hannett, more usually associated with Joy Division and Buzzcocks, is named by Biafra in the opening of the In God We Trust, Inc. version of the song, held as having "overproduced" the production. The mention was intended as ironic, as Hannett never worked with the Dead Kennedys. He was just a widely respected and iconic engineer they just wanted to mention.