Morality is commonly held up as the pinnacle of goodness but can also be a source of significant problems, interfering with societal functioning and progress. We review the literature regarding how morality diverges from nonmoral attitudes, biases our cognitive processing, and the ways in which it can lead to negative interpersonal and intergroup consequences. To illustrate the negative implications of morality, we detail two specific examples of how moral convictions impair societal progress: the rejection of science and technology, and political polarization in the United States. Specifically, we discuss how moral convictions can cause individuals to challenge scientific facts (e.g., evolution), oppose technologies that can improve health and well‐being (e.g., vaccinations and GMO foods), and fuel political polarization and segregation. We conclude this review by suggesting strategies for policy makers and individuals to help overcome the problems morality can cause.