Do people apply different standards of consistency to different kinds of beliefs? For instance, are religious beliefs judged more tolerant of inconsistency than factual beliefs? In two preregistered studies (Ns=181, 195), we investigated norms for consistency by asking participants to evaluate pairs of contradictory beliefs held simultaneously by a single person. In both studies, holding inconsistent beliefs was overwhelmingly judged to be irrational. Study 1 found differences in judgments across domains, and Study 2 identified features of beliefs likely to drive this variation: participants judged inconsistency as more rational when both beliefs were seen as containing some truth and when there was more uncertainty concerning which belief was correct. (In contrast to motivated reasoning accounts, belief desirability did not independently predict judgments). Participants also distinguished how inconsistencies should be resolved across domains, recommending obtaining more information to resolve factual and political inconsistencies, but thinking more for moral, religious, and preferential inconsistencies. Finally, explaining how a person could hold inconsistent beliefs reliably increased the perceived rationality of those beliefs. Together, these findings suggest that inconsistencies are generally viewed as irrational, but with some leeway governed by the epistemic characteristics of particular beliefs and whether inconsistencies are explained. Our results have implications for theories of the nature of belief, the folk psychology of belief attribution, and research on interpersonal disagreement.