We propose that social psychological findings on the intuitive bases of moral judgment have broad implications for moral education. The "five foundations theory of intuitive ethics" is applied to explain a longstanding rift in moral education as an ideological disagreement about which moral intuitions should be endorsed and cultivated. The Kohlbergian moral reasoning side has sought to limit the domain of moral education to Harm and Fairness-related moral concerns, whereas character education approaches have tried also to cultivate intuitions concerning the Ingroup, Authority and Purity foundations. Recent attempts to merge the two lines of moral education have not fully addressed this ideological rift, for example by delineating how a single approach could reconcile opposing group- and individual-focused conceptions of moral education. We conclude that psychological research on moral intuition offers a descriptive account of human morality that reveals problems with attempts to create a normative basis for moral education from either side of the ideological divide.