In much contemporary political discourse, valued cultural characteristics are threatened by interaction with culturally-distinct others, such as immigrants or a hegemonic majority. Such interaction often fosters cross-cultural competence (CCC), the ability to interact successfully across cultural boundaries. However most theories of cultural dynamics ignore CCC, making cultural diversity incompatible with mutually-beneficial inter-group interaction, and contributing to fears of cultural loss. Here, new theory, incorporating competing developmental paths to CCC and group identity valuation, illuminates how a common strategy of disempowered minorities can counter-intuitively sustain cultural diversity: Given strong group identity, minorities in a structurally-unequal, integrative society can maintain their distinctive cultural norms by learning those of the majority. Simple field methods in an Amazonian population demonstrate how to assess such strategies' effectiveness given predicted dynamics.