While previous studies reveal mixed findings on the relationship between analytic cognitive style (ACS) and right-wing (conservative) political orientation, the correlation is generally negative. However, most of these studies are based on Western, educated, industrialized, rich, and democratic (WEIRD) societies, and it is not clear whether this relationship is a cross-culturally stable phenomenon. In order to test cross-cultural generalizability of this finding, we re-analyzed the data collected by the Many Labs 2 Project from 30 politically diverse societies (N = 7,263). Social conservatism is measured with the binding foundations scale, comprising of loyalty (patriotism), authority (respect for traditions), and sanctity (respect for the sacred), as proposed by the moral foundations theory, while ACS is measured by the three-item modified cognitive reflection task. The level of WEIRDness of each country was calculated by scoring how much a culture is Western, educated, industrialized, rich, and democratic. Although social conservatism is negatively associated with ACS in the aggregate, analysis indicates that the relationship is significantly stronger among WEIRD and remains negligible among non-WEIRD cultures. These findings show the cross-cultural variability of this relationship and emphasize the limitations of studying only WEIRD cultures.