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, interview-based field methods at an Amazonian ethnic boundary demonstrate the prevalence of CCC. These data motivate a new theoretical mathematical model, incorporating competing developmental paths to CCC and group identity valuation, that illuminates how a common strategy of disempowered minorities can counter-intuitively sustain cultural diversity within a single generation: Given strong group identity, minorities in a structurally unequal, integrative society can maintain their distinctive cultural norms by learning those of the majority. Furthermore, rather than a rejection of, or threat to, majority culture, the valuation of a distinctive minority identity can characterize CCC individuals committed to extensive, mutually beneficial engagement with the majority as members of an integrative, multi-cultural society.