Minority rights have come under increasing pressure in several established liberal democracies, often with limited public resistance. This is puzzling, as citizens are typically viewed as safeguards against undemocratic actions and consistently express strong support for minority rights. One explanation is that prior research measures such support in isolation, overstating commitment. In practice, democratic principles can conflict, requiring tradeoffs. Yet we know little about how citizens respond under such conditions. This study examines a core tension between the liberal and majoritarian components of democracy from the perspective of citizens. Using a novel tradeoff measure, it captures preferences over the balance between minority rights protection and majority rule and identifies factors associated with positions that may undermine this balance. Data from 15 countries show that, when forced to choose, citizens are less committed to minority rights than previously assumed. Respondents who identify as members of certain minority groups, as well as those endorsing nativist or authoritarian beliefs, exhibit polarized preferences, prioritizing either minority rights or majority rule to the point of jeopardizing the opposing principle. Age, political knowledge, and populist beliefs are associated with inconsistent preferences across measurement approaches, with some individuals reversing their positions depending on framing. These findings refine our understanding of public commitment to liberal democratic principles, highlight implications for the measurement of political attitudes, and demonstrate how incumbents and far-right parties can exploit such tradeoffs to justify the erosion of democratic norms.