Electoral gender quotas remain contentious among many publics. One hurdle is the “principle-policy puzzle”: those who espouse gender egalitarianism may nevertheless oppose affirmative action measures because of disagreements about their necessity and worries about government overreach. Based on an original survey in Japan, where women’s underrepresentation is particularly pronounced, we identify two dimensions that drive attitudes toward quotas. First, modern sexism matters: those who attribute underrepresentation to women’s disinterest or who think that quotas will increase the number of unqualified women candidates are less likely to support quotas. Second, appropriateness matters: those who oppose government intervention in gender affairs are less likely to support quotas. Crucially, these differences hold even among those who desire more women in parliament. Our results suggest that public acceptance of quotas depends more on correcting misperceptions about structural gender barriers and the benign consequences of quotas (“policy”), rather than encouraging people to prefer more women in parliament (“principle”).