Nope, you're not wrong, although I know several right wing folkies (Peter Bellamy was one of the more famous and I'm pretty sure Bob Copper was a traditional working class Conservative) in the main it is left leaning. There are all sorts of reasons for this; the singing is rooted in the community, the pub, the chapel, the workplace, the music hall etc. the very places where socialism first grew and flourished. It was looked down on by the upcoming middle classes as common and not as good as 'proper' music (an attitude that still exists today amongst some parts of the classical music audience in this country, odd when they'll listen to Schubert's settings of German folk songs but dis Britten or Granger's efforts at the same, but, I have to say, there is an inverted snobbery in some parts of the folk music scene on the same subject). But mainly because the post war Folk Revival was driven by the same people as were active in such organisations as CND and the various socialist parties who have somewhat commandeered it. Nowadays performers tend to be those for whom socialism is an attractive option, people living from hand to mouth on very low incomes, travelling round the country performing in subsidised halls, possibly with grants from supporting Arts charities and quangos, and educated at the States expense with degrees in useless subjects like Folk Studies, Music, etc. Many of them have first hand experience of the inequalities of life and are stupid (or idealistic) enough to think that they might make a difference.
One of the reasons why the founders of the Folk Revival and their descendants have such an antipathy to the right wing is because in the early days of that revival the right wing actively discouraged the flowering of the rennaissance of the music by insisting that it was all old hat and not worth bothering with; that Britain needed a new music and not harkening back to the good old days, and continue to do so by reducing everything to economic terms by insisting on the withdrawal of financial support for places where the music can be heard, from withdrawing financial support from any education that doesn't have strict economic benefits and by withdrawing financial support for the performers whilst they are learning their trade. It seems a bit rich to them that the section of the community that has done least to support the music should then try and take advantage of it for their own political ends.
Not that I'm trying to be controversial or anything.

Currently investigating the Hillmans of Sussex.