the constitution stipulated that the governor was required to “declare himself to be of the Christian religion” (Constitution of…, II.II.I.II, emp. added), and that any who wished to serve as governor, lieutenant governor, counselor, senator, or representative were required to take an oath of office which included: “I…do declare that I believe the Christian religion, and have a firm persuasion of its truth” (Constitution of…, II.II.V.I, emp. added).Besides Jews and Muslims, these provisions also of course prevented atheists, deists and theists from being officials. Arguably it excluded Unitarians such as John Adams, once president of the US. (People differ on what it means to be "a Christian.")
You will find people on FR who exclude Mormons, Catholics and others.