‘Functional’ diversity is believed to influence ecosystem dynamics through links between organismal traits and ecosystem processes. Theory predicts that key traits and high trait redundancy – large species richness and abundance supporting the same traits – can buffer communities against environmental disturbances. While experiments and data from simple ecological systems lend support, large‐scale evidence from diverse, natural systems under major disturbance is lacking. Here, using long‐term data from both temperate (English Channel) and tropical (Seychelles Islands) fishes, we show that sensitivity to disturbance depends on communities’ initial trait structure and initial trait redundancy. In both ecosystems, we found that increasing dominance by climatically‐vulnerable traits rendered fish communities more sensitive to environmental change, while communities with higher trait redundancy were more resistant. To our knowledge, this is the first study demonstrating the influence of trait structure and redundancy on community sensitivity over large temporal and spatial scales in natural systems. Our results exemplify a consistent link between biological structure and community sensitivity that may be transferable across ecosystems and taxa and could help anticipate future disturbance impacts on biodiversity and ecosystem functioning.