Sexual dimorphism is a ubiquitous source of within-species variation, yet the community-level consequences of sex differences remain poorly understood. Here, we analyse a bitrophic model of two competing resource species and a sexually reproducing consumer species. We show that consumer sex differences in resource acquisition can have striking consequences for consumer-resource coexistence, abundance and dynamics. Under both direct interspecific competition and apparent competition between two resource species, sexual dimorphism in consumers' attack rates can mediate coexistence of the resource species, while in other cases can lead to exclusion when stable coexistence is typically expected. Slight sex differences in total resource acquisition also can reverse competitive outcomes and lead to density cycles. These effects are expected whenever both consumer sexes require different amounts or types of resources to reproduce. Our results suggest that consumer sexual dimorphism, which is common, has wide-reaching implications for the assembly and dynamics of natural communities.