If folk songs include anything vaguely musical that is transmitted orally (and Mudcatters tend to be an inclusive lot) then some right wing nerd should be collecting the vile racist chants heard at football matches when black players are on the field.

And there are plenty of examples of Nazi songs (right wing enough?) that went, for a time, into popular tradition in Germany. The first time I heard 'The Horst Wessel Lied' I thought it had a really terrific tune and the lyrics struck me as inspiring. Trouble was, 'terrific' meant spreading terror and 'inspiring' meant inspiring hatred.

At the lighter end off the right wing spectrum - I agree with musicmic that many of the most amusing, seemingly anti-left songs (Arry Pollit is a good example) were actually sung with gusto by the farthest left of the lefties. See Digitrad 'The Foreman's Job' and related threads for parodies of The Red Flag - and add

The People's flag is palest pink
And not as red as you lot think.

The left has always been moderately good at self-mockery.