The Cathars were mostly tolerated by the local authorities and nobility in the south of France though. The Albigensian were basically a land grab by the nobles in northern France in expense of their souther brethren and nothing more (why would the catholic king of Aragon and the count of Toulouse fight on the side of the Cathars otherwise?)
You raise a point worth discussing. In our contemporary times there are more traditional political factions and local authorities in the USA who believe in the legitimacy of the United States political process or at least the constitution (many sovereign citizens don't, preferring the articles of confederatin) yet are also more sympathetic to sovereign citizens than their counterparts, and could be interested in temporary alliances with them if trouble broke out. At the end of the day, Aragon remained under Catholic authority either way, but wanted to use tolerance of the Cathars as a wedge to keep hold of territory. Similarly, I could imagine a rural law-abiding United States bloc preferring that, for economic or political reasons, there be a nearby commune of Sovereign Citizens who are strange, under-documented, and sometimes live in potentially hazardous conditions, but are friendly and willing to pitch in to help the broader community out of a shared sense of common "American freedomism" so long as law enforcement and other day-to-day restrictions aren't carried out in ways they consider illogical or intrusive.
Those religious lines, especially during "wars of religion" start to get blurry pretty quick. In the 30 years war France, Catholic, fought with the Swedes, Protestant, against the Habsburgers, Cathloic. Why? Because France didn't like the idea of having a Habsburg empire to its south, Spain, and west, Germany.
