What term is used to describe a prolonged and often bitter dispute or argument?

The term that describes a prolonged and often bitter dispute or argument is "schism." This word specifically refers to a division or separation, particularly within groups or organizations, often due to conflicting differences that lead to a prolonged conflict. Schisms can occur in various contexts, such as religious organizations, political parties, or even personal relationships, where deeply held beliefs or opinions create a rift that results in ongoing disagreement and contention.

In contrast, the other terms provided do not share this meaning. "Skeptical" refers to a doubtful or questioning attitude towards something. "Satiate" means to satisfy fully or beyond capacity, and "sanctimonious" describes someone who makes a show of being morally superior to others. None of these terms convey the idea of a prolonged and bitter dispute. Thus, "schism" is the appropriate choice for this definition.