The Inquisition in Spain was targeted against people who claimed to be Catholic but were secrete Muslims and seen as a third column against the Crown, who had just won the 700 year old Reconquista.
There was the Calvinist Inquisition by Jean Calvain in Geneva, and the Puritans were conducting their own inquisitions in England and Scotland under Cromwell and in some of the North American colonies.
Yes, torturing and killing people of another faith is just what The One True Apostolic Church would do. Just doing Gods work, no doubt.