Especially when the Papacy and some order or another conflicted. Example: The Franciscans took their clerical vow of poverty very seriously, and were offended by the luxury and wealth of the Papacy. At the beginning of the 14th century, the Franciscans began to argue the absolute poverty of Christ, that he literally owned nothing. Everything he had was given to him by a supporter. The Papacy, which was quite extravagant at the time, rejected this idea, and Benedict XIII eventually banned the order over this issue and their criticism of Papal wealth. Franciscans found easy and frequent refuge with powers who we not in lock step with Rome, such as in England, and in the Empire. William of Ockham was one of these Franciscans who fought with the Pope. The struggles of the Franciscans got intertwined with other anti-Papal struggles like the fight between Louis the Bavarian (who spent a great deal of his reign excommunicated, though supported not only by the Franciscans but by the German church as well) and the Anglo-French conflicts.

That's an extreme example, where an order got banned, but you can easily imagine other conflicts that were less intense, or happened to overlap less with other critical fights.