The most likely scenario I can think of is a Druze-type situation, in which the Cathars retreat to mountain fortresses while pledging not to proselytize among the Catholics, in return to being left alone by the Church. Now, the POD for such a scenario would IMO have to be before the Albigensian crusade, since by that point it would already be too late to dissuade the Pope from trying to convert the heretics by force.