Face masks are one of the cheapest and most effective non-pharmaceutical interventions available against airborne diseases such as COVID-19. Unfortunately, they have been met with resistance by a substantial fraction of the populace, especially in the U.S. In this study, we uncover the latent moral values that underpin the response to the mask mandate, and paint them against the country's political backdrop. We monitor the discussion about masks on Twitter, which involves almost 600k users in a time span of 7 months. By using a combination of graph mining, natural language processing, topic modeling, content analysis, and time series analysis, we characterize the responses to the mask mandate of both those in favor and against them. We base our analysis on the theoretical frameworks of Moral Foundation Theory and Hofstede's cultural dimensions. Our results show that, while the anti-mask stance is associated with a conservative political leaning, the moral values expressed by its adherents diverge from the ones typically used by conservatives. In particular, the expected emphasis on the values of authority and purity is accompanied by an atypical dearth of in-group loyalty. We find that after the mandate, both pro- and anti-mask sides decrease their emphasis on care about others, and increase their attention on authority and fairness, further politicizing the issue. In addition, the mask mandate reverses the expression of Individualism-Collectivism between the two sides, with an increase of individualism in the anti-mask narrative, and a decrease in the pro-mask one. We argue that monitoring the dynamics of moral positioning is crucial for designing effective public health campaigns that are sensitive to the underlying values of the target audience.