Effective response to pandemics requires coordinated adoption of mitigation measures, like masking and quarantines, to curb a virus's spread. However, as the COVID-19 pandemic demonstrated, political divisions can hinder consensus on the appropriate response. To better understand these divisions, our study examines a vast collection of COVID-19-related tweets. We focus on five contentious issues: coronavirus origins, lockdowns, masking, education, and vaccines. We describe a weakly supervised method to identify issue-relevant tweets and employ state-of-the-art computational methods to analyze moral language and infer political ideology. We explore how partisanship and moral language shape conversations about these issues. Our findings reveal ideological differences in issue salience and moral language used by different groups. We find that conservatives use more negatively-valenced moral language than liberals and that political elites use moral rhetoric to a greater extent than non-elites across most issues. Examining the evolution and moralization on divisive issues can provide valuable insights into the dynamics of COVID-19 discussions and assist policymakers in better understanding the emergence of ideological divisions.