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We study the evolution of cultural divides both theoretically and empirically. We propose a model of cultural change where intergenerational transmission and forces of social influence determine the distribution of cultural traits in society. We conduct an empirical investigation of the evolution of cultural heterogeneity in the USA between 1972 and 2018, using the General Social Survey. In recent decades, cultural heterogeneity between individuals has risen. Cultural divides between identity groups display contrasted patterns: increasing along lines of religion and political orientation, mildly U-shaped along income and racial lines, and flat or decreasing for gender and urbanicity. We interpret these empirical findings in light of our model, arguing that changes in modes of interaction within and across groups can explain the observed dynamics of cultural heterogeneity.