I've been thinking about this topic for a while. Most (certainly not all, but most) of the "left wing" folk songs that are generally ttthought of date back to the era between WWI and WWII. During that period, group singing was popular--I remember "follow the bouncing ball" singalongs at the neighborhood movie houses between features--and the organized left-wing groups, from the IWW to the Communist Party made use of this by having topical songs composed. They weren't the only ones, though. Many companies (I recall IBM, GE and Fuller Brush) had songbooks for their employees, which preached their obviously right-wing sentiments, usually as parodies of well-known songs: "There's a place in my heart that no other can fill, for a company that's fair and can boast of good will...", to the tune of Mother Machree.
Similarly, colleges, high schools and even elementary schools had songs praising these establishments. And if we're discussing "folksong" that expresses right-wing (read conservative) sentiment, there's the vast body of hymns and gospel songs.
Earlier, during the Civil War, say, there were songs ardently espousing both sides; the same thing occured in the American Reolutionary War.....
I guess my thesis is that folks sing all sorts of stuff, while collectors do a great deal of filtering. Sharp and bBaring-Gould undoubtedly collected a vast amount of bawdy material, but deleted or bowdlerized it in their published collections; just about every collector (with the blessed exception of Randolph) simply refused to collect songs that the fols sang that the collector didn't consider "folk" and most of the other collectors in the 30's to 50's had a strong leaning towards the political left, and collected accordingly.