Socio-diversity, the variety of human opinions, ideas, behaviors, and styles, has profound implications for social systems. This paper studies how fundamental characteristics of social networks can support or hinder socio-diversity using models of cultural evolution, mathematical analysis, and numerical simulations. We find that pronounced inequalities in the distribution of connections obstruct socio-diversity, while close-knit communities, scarce long-range connections, and higher tie density tend to promote it.