It would pretty much have to be based on a successful and coinsciously new religion. Rural communities in European histpry have pretty much always been heterodox in religious terms, but crucially, they didn't see it that way. As far as the good folk of Montaillou were concerned, they were good Christians and Catholics, however much the Inquisition begged to differ. That means uniting them will be a hopeless cause - they'd regard each other as heretics and filthy foreigners.
Political interest is a possibility, but it is hard to see how it could organise itself. Even as late as the Peasant War of 1525, religion played a major role.
I think one good opportunity would be in the course of the 'apostolic poverty' waves of the 11th-13th centuries. Rural communities were less affected than the urban poor, but it could easily spread and lead some of them to form into a community that rejects aristocratic power and wealth. Find a bishop who's willing to tolerate them (and an area that is distant or inaccessible enough for them to be unbothered), and you're in business. It's noit as far-fetched as it seems, the popes were quite ready to make deals with rebels if they felt unthreatened, and the Franciscans almost got branded heretics before becoming pillars of the Church.
An alternative would be a more successful 15th century anticlerical movement holding on. Wiclif, Hus and a myriad forgotten others held ideas that could find broad acceptance among the peasantry if advertised right. I'm not sure the English Peasant Revolt had the opportunity - its heartland is too accessible and the state too powerful - but the mountains of the north, the Appenines, Alps, Carpathians, Massif Central or such, the plains and islands of the North Sea coast or the eastern borderlands with the Orthodox and Ottomans would be possible locations.