Traditional public opinion research suggests that average citizens are non-ideological or ideologically moderate, with only a sophisticated minority exhibiting constrained political beliefs. Challenging this view, we propose focusing on citizens’ meta-cognitive beliefs about ideological consistency among other people — a phenomenon we refer to as first-order, or ‘projected’ belief constraint. Leveraging belief network analysis on experimental data, we show that citizens overestimate the degree of ideological alignment in strangers, perceiving them, on average, as more streamlined than they are based on their actual, self-held beliefs. Our preliminary results further show that ideological "overprojection" cannot solely be explained by individuals’ own levels of issue constraint. The tendency to over-project ideological alignment, we argue, may have significant implications for interpersonal behavior, potentially contributing to prejudiced inter-group interactions and affective polarization. In this registered report manuscript, we present the results of an initial pilot study measuring the degree of ideological over-projection and outline an experimental design to test the downstream behavioral consequences of ideological projection. Our study aims to enhance scholarly understanding of ideological thinking and to device strategies to reduce issue-based hostility in daily interactions between members of different partisan-ideological groups.