"Yankee Doodle" started out as a song mocking the colonists. They adopted it as their own, making it a political statement. It certainly is part of the folk idiom in the US.

Children's rhymes, such as "Four and Twenty Blackbirds" and "Little Jack Horner" are also relevant here, as they can have political protest meanings (and these two do).

I suspect that ofttimes it depends upon the context. "Wait for the Wagon" is a perfectly good song from the 19th C. US -- but when changed to "...the dissolution wagon" it back a political song of the South during the US Civil War.

Burns' "Bonnie Dundee" was overtly political; during the US Civil War it became "Riding A Raid" and continued as such. It could be argued that in its incarnation as "Lords of the Cam" (Girton College, Cambridge, ca. 1870) it was again political, although not warmongering, as it was used to support the awarding the BA to women.

So...I suppose it depends. "Lillibulero" was just a song before 1689 and all that.