The Cathars:  Cathar Beliefs:  Roman Catholic Propaganda:  Bestiality.

There is no evidence that Cathars were given to practice Bestiality. 

The accusation is based on the idea that heretics were interested in, and given to kissing, the backside of cats.  There seems to be no genuine evidence for this practice, nor any plausible explanation of how the accusation arose. One Catholic Authority, writing about 1182, tells us about "many" reformed Cathars who admitted that at night groups of heretics :

... sit waiting in silence in their respective synagogues, and a black cat of marvellous size climbs down a rope which hangs in their midst. On seeing it, they put out the lights. They do not sing hymns or repeat them distinctly, but hum them through clenched teeth and pantingly feel their way toward the place where they saw their lord. When they have found him they kiss him, each the more humbly as he is the more inflamed with frenzy - some the feet, more under the tail, most the private parts. And, as if drawing license for lasciviousness from the place of foulness, each seizes the man or woman next to them, and they commingle as long as each is able to prolong the wantonness.

Walter Mapp was the Chancellor of the Bishop of Lincoln. Here he is referring to "Publicans or Patarnes", names by which Cathars were known to Roman Catholic authorities. The quotation is from his "Courtier's Trifles, De nugis curialium I.xxx edited by Montague R James (Anecdota oxoniensa..., medieval and modern series, XIV (Oxford, 1914) pp 57-59. English translation based on wakefield & Evans, Heresies of the High Middle Ages, §42B, p254.

It is notable that such accusations were made against other groups that the Roman Church regarded as its enemies.  For example, the same accusation was used a century later against the Knights Templars and then against supposed witches.    One factor is that Catholics imagined that the devil liked to adopt the form of a cat - which also explains why cats are still associated with witches in the mainstream Christian mind.

The most likely explanation seems to be the fevered imagination of some unknown medieval churchman.  All it would take was one deranged Episcopal inquisitor plagued by fantasies of the feline podex.  Such an Inquisitor could extract whatever confession he wanted from anyone who came into his power.  The confession would then establish an accepted view of how heretics and the devil operated.  This could be confirmed by any number of further confessions extracted under torture or duress.  Positive feedback loops like this proved any number of unlikely accusations - sailing in sieves, flying through the air, taking animal form, demonic visitations, and so on.

The name Cathar may be derived from a German word referring to this particular calumny about cats' backsides, but it rather backfired when everyone assumed that the name must come from the Greek word for pure.