Methodists were quite definitely non-conformists, probably the most important group of such in England. Nowadays much in decline.
Despite being a raging atheist, I don't have any problem with people singing hymns during folk concerts, as long as there aren't too many of them and they are good songs. I've never agreed with General Booth's comment on the devil and good tunes, there's some great stuff in the religious traditions. I used to love "Hills of the North Rejoice" at school, though thinking it could be usefully revived as part of a campaign for Northumbrian nationalism.
And Maddy Prior's Xmas carol concerts with the medieval band were something special. (I'll remember the band's name immediately after signing off. The Harvest band?)