Literature in the area of social networks indicates that increases in perceived social network attitudinal heterogeneity generate increased openness to attitude change. Recent evidence in the area of morality, however, shows that morally based attitudes are particularly resistant to persuasion and can result in the rejection of disagreeing others. Positing that considering morality would reduce network influence, an experiment varied moral cues presented along with a non-network persuasive message while holding the actual content constant. Results demonstrate that morality and network composition interact to predict persuasion, such that when people are not cued to consider morality increased network heterogeneity predicts increased persuasion, but when identical messages are presented in a way that invokes morality the impact of network heterogeneity disappears or even reverses marginally. This interactive effect was replicated in two very different political issues: gay adoption and nationalized healthcare. Implications for persuasion by morally motivated sources independent of the effects of specific moral arguments are discussed.