We investigate public preferences for equity-enhancing policies in access to early child care, using a survey experiment with a representative sample of the German population (n ≈ 4, 800). We observe strong misperceptions about migrant-native inequalities in early child care that vary by respondents' age and right-wing voting preferences. Randomly providing information about the actual extent of inequalities has a nuanced impact on the support for equity-enhancing policy reforms: it increases support for respondents who initially underestimated these inequalities, and tends to decrease support for those who initially overestimated them. This asymmetric effect leads to a more consensual policy view, substantially decreasing the polarization in policy support between under- and overestimators. Our results suggest that correcting misperceptions can align public policy preferences, potentially leading to less polarized debates about how to address inequalities and discrimination.