The Spanish Inquisition investigated Catholics only. It left followers of other faiths alone. But if you a Jew who converted to Catholic Christianity because of the difficulties (or, finally, impossibility) of being a Jew in Spain, but then kept kosher or gave signs of not really believing the Catholic faith, then you came to the Inquisition. You weren't tried for not believing, you were tried for pretending to believe.
Compared to the other jurisprudence of the times, the Inquisition provided far more due process. The number of victims of the Inquisition, though even one is too many, is dwarfed by the tens of thousands killed for witchcraft, which was often tried by ordeal rather than the taking of evidence.
I got my first dose of this data from a talk by a UVA history professor who began his studies of the Spanish Inquisition as a non-Catholic. When he found how thick and many the lies were against the Catholics, it enticed him to look further into the Catholic CHurch, and he became a Catholic a few years ago.
My other source is a Ph. D. Candidate who gave a talk when he was on a short trip to Charlottesville from Spain where he is researching. He is a 'cradle Catholic'.
The Albigensians of 800 years ago pre-existed the modern nation state and were considered a political threat as well as a threat to the Church. One of the stories of Dominic's early ministry is of his spending all night talking the Albigensian innkeeper where he was staying into returning to orthodoxy.
One thing we can conclude from this is that Albigensians and Catholics coexisted in Southern France and Northern Italy for quite some time. The Albigensians had enough freedom of movement to kill Peter of Verona, one of the first Dominican martyrs -- one of whose killers repented and joined the order as a lay brother.
Yes there was a massacre. But how much that was a matter merely of religion and how much a matter of a threat to the uneasy and changing feudal order is not clear.