Quantifying the distance between cultural groups has received substantial recent interest. A key innovation borrowed from population genetics has been the calculation of cultural Fst (CFst) statistics (Bell, et al. 2009) on datasets of human culture. Measuring the variance between groups as a fraction of total variance, Fst's are theoretically important in additive models of cooperation, where they have positive marginal effects on selection for altruism. Consistent with this, recent empirical work has confirmed high values of pairwise CFst (measuring cultural distance) strongly predict unwillingness to cooperate with strangers in coordination vignettes. As applications for Fst increase, however, there is greater need to understand their meaning in naturalistic situations beyond additive cooperation. Traditionally studied in evolutionary game theory with models such as Stag Hunt, Hawk-Dove, Snowdrift, and Chicken, these interactions can be characterized by both positive and negative frequency-dependence, and by the presence of high-diversity, mixed equilibria. Abstracting across such games to a general model of linear synergy, we derive a simple relationship between Fst and the evolution of group-beneficial behaviors across a broad spectrum of social interactions. By making explicit the relationship between population structure and the evolutionary outcomes of social interactions with synergistic dynamics, we provide broader theoretical support for empirical applications of CFst, and motivate new questions in the evolutionary study of culture that bridge the topics of synergy, network associativity, the complexities of identity, and the paradox of cultural diversity.