To my recollection, there were a number of states with alternative religious bodies that were not directly under the Papal Hierarchy. Of course, one could read a large body of writings on any number of the subjects I raised, but I hope it can be a useful introduction to the later Medieval period.
- Southern Italy & the Normans (10th-12th Century) - While the Normans were off-and-on rivals of the Popes & HRE Emperors, they did acquire a number of non-Latin vassals in the Kingdom of Sicily. There remained Eastern (Byzantine) Christians who followed the Constantinoplitan rite even after the Byzantine presence was removed by the Saracens in the 8th & 9th Century. Furthermore in Sicily, the Normans acquired a number of Muslim subjects, who did not immediately "convert" to Latin Catholicism for a number of decades.
- The Reconquista & Northern Kingdoms (10th-15th Century) - Similar to the Normans, the Kingdoms of Leon, Portugal, Castille, and Aragon acquired a number of non-Christian subjects in the 11th-13th century. It would not be until the 15th century that the Spanish Inquisition & expulsion of the Moors began in vigor, so it stands to reason that the Northern Kingdoms had some substantial Muslim population.
- Lithuania & the Eastern Orthodox (14th-16th Century) - As the Dukes of Lithuania advanced Eastward and checked the Golden Horde at the Battle of Blue Waters (1362), they advanced into the fragmented remains of the former Kieven Rus. As such, they acquired a number of Eastern Christians who remained out of communion with the Papacy. The Lithuanian-Polish Commonwealth would later seek to restore the Eastern Christians into communion (Union of Brest, 1595), so for a period of several hundred years, Eastern Christians were underneath a Roman Catholic aristocracy.
- Kingdom of Bohemia & Hussites (15th Century) - Though on the tale end of the "Medieval Age", the case of John Hus & the Council of Constance is a good example of a persistence "non-Papal" Latin Christianity resisting Papal Control. Despite repeated diplomatic & military attempts to resolve the Hussite controversy, a majority of Bohemian rulers tolerated the Hussites until the Reformation & Wars of Religion.