Most research on public opinion assumes that American political views are structured by a belief system with a clearly-defined liberal-conservative polarity; however, this is not true of all Americans. In this article we document systematic heterogeneity in the organization of political attitudes and explain its basis in the sociodemographic profile of the respondents. We use Relational Class Analysis (RCA), a network-based method for detecting heterogeneity in collective patterns of opinion, to identify distinctive belief networks, each shared by a different group of respondents. Analyzing ANES data between 1984 and 2004, we identify three groups of American citizens: Ideologues, whose political attitudes strongly align with either liberal or conservative categories; Alternatives, who are instead morally conservative but economically liberal, or vice versa; and Agnostics, who exhibit weak associations among political beliefs. Respondents' sociodemographic profiles, particularly their income, education, and religiosity, lie at the core of the different ways in which they understand politics.