The Cathar Heresy

This is the first time I've ever heard it suggested that we don't know what the Cathars believed.

“Cathars”–the target of (a) the first intra-Europe crusade... that resulted in the deaths of tens of thousands (often by fire) and the desolation of vast swathes of southern France, and (b) an inquisition that killed more–are a source of fascination and mystery. They left little of a written record, and most of that which is “known” about them was written by a Catholic Church that ruthlessly persecuted them as “heretics.” Thus, what their “heresies” actually were is unknown.

In his fascinating The Rest is History Podcast, historian Tom Holland conjectures that their heresies had nothing to do with dualism or celibacy... they were in a way proto-Protestants who believed that salvation was not dependent on the intermediation of priests, bishops, archbishops, and Popes. One could become a “bon homme” destined for heaven by one’s own conduct and faith without priestly intermediation. This clashed with Pope Innocent III’s aggressive centralizing efforts to enforce the primacy of the priesthood and the formal church.

Put simply, this was a clash between self-governing rural traditionalists and an extremely assertive–and in fact murderous–bureaucratic government with universalist pretensions insistent on controlling the private and public lives of everyone.

(H/t Hot Air). You can read a summary of what we commonly teach that they believed at Wikipedia. You can read an extended analogy to the present conflict at the first link. 

UPDATE: Dad29 sends this from an older edition of the Catholic Encyclopedia he had on hand:

The essential characteristic of the Catharist faith was Dualism, i.e. the belief in a good and an evil principle, of whom the former created the invisible and spiritual universe, while the latter was the author of the material world. A difference of opinion existed as to the nature of these two principles. Their perfect equality was admitted by the absolute Dualists, whereas in the mitigated form of Dualism the beneficent principle alone was eternal and supreme, the evil principle being inferior to him and a mere creature. In the East and the West these two different interpretations of Dualism coexisted. The Bogomili in the East professed it in its modified form. In the West, the Albanenses in Italy and almost all the non-Italian Cathari were rigid Dualists; mitigated Dualism prevailed among the Bagnolenses and Concorrezenses, who were more numerous than the Albanenses in Italy, though but little represented abroad. (For an exposition of absolute Dualism, see ALBIGENSES; on the mitigated form, see BOGOMILI.) Not only were the Albanenses and Concorrezenses opposed to each other to the extent of indulging in mutual condemnations, but there was division among the Albanenses themselves. John of Lugio, or of Bergamo, introduced innovations into the traditional doctrinal system, which was defended by his (perhaps only spiritual) father Balasinansa, or Belesmagra, the Catharist Bishop of Verona. Towards the year 1230 John became the leader of a new party composed of the younger and more independent elements of the sect. In the two coeternal principles of good and evil he sees two contending gods, who limit each other's liberty. Infinite perfection is no attribute even of the good principle; owing to the genius of evil infused into all its creatures, it can produce only imperfect beings. The Bagnolenses and Concorrezenses also differed on some doctrinal questions. The former maintained that human souls were created and had sinned before the world was formed. The Concorrezenses taught that Satan infused into the body of the first man, his handiwork, an angel who had been guilty of a slight transgression and from whom, by way of generation, all human souls are derived. The moral system, organization, and liturgy of absolute and mitigated Dualism exhibit no substantial difference, and have been treated in the article on the Albigenses.

The philosophical argument against Dualism, by the way, is that it is impossible. If there were a Good principle and also an Evil principle that defined the universe between them, there would still have to be a third thing that was the substrate that existed which allowed them to interact. The third thing would then be prior to both of the so-called 'first principles,' and being prior, would itself be the First Thing. 

There can't be any other number of multiple first principles for this same reason. The Highlander tag line was "There can be only One," but in fact it was known since Ancient Greece. It was stated in theological form by Avicenna in his Metaphysics of the Healing.