Income distributions across countries vary substantially, and within countries, preferences for redistribution vary across the population. Moreover, they are correlated with characteristics such as political views, personal income, and beliefs. Equality is a furiously debated topic in public and in these debates simple justice principles are evoked to motivate and solidify positions. From an academic perspective, the clearest expression of such principles applied to income distributions are so-called social choice axioms. Building on the methodology of Nielsen and Rehbeck (2022), we ask from a positive perspective: What kind of sets of basic distributive social choice axioms people subscribe to? Which principles do their distributive choices respect? And if these are in conflict, how do people resolve such a conflict? Additionally, we correlate the preferred sets of axioms, preferred distributive choices, and the resolutions of conflict with demographics, political orientations, and redistributive policy preferences. We propose a basic typography of disagreement in society and investigate whether societal conflict is more or less pronounced when people have resolved their personal conflicts. We also shed light on differences across demographic groups. Our findings offer insights that may facilitate to better understand the optimal elicitation of redistributive and policy preferences in empirical research.