Global climate change is altering community composition across many ecosystems due to nonrandom species turnover, typically characterized by the loss of specialist species and increasing similarity of biological communities across spatial scales. As anthropogenic disturbances continue to alter species composition globally, there is a growing need to identify how species responses influence the establishment of distinct assemblages, such that management actions may be appropriately assigned. Here, we use trait‐based analyses to compare temporal changes in five complementary indices of reef fish assemblage structure among six taxonomically distinct coral reef habitats exposed to a system‐wide thermal stress event. Our results revealed increased taxonomic and functional similarity of previously distinct reef fish assemblages following mass coral bleaching, with changes characterized by subtle, but significant, shifts toward predominance of small‐bodied, algal‐farming habitat generalists. Furthermore, while the taxonomic or functional richness of fish assemblages did not change across all habitats, an increase in functional originality indicated an overall loss of functional redundancy. We also found that prebleaching coral composition better predicted changes in fish assemblage structure than the magnitude of coral loss. These results emphasize how measures of alpha diversity can mask important changes in the structure and functioning of ecosystems as assemblages reorganize. Our findings also highlight the role of coral species composition in structuring communities and influencing the diversity of responses of reef fishes to disturbance. As new coral species configurations emerge their desirability will hinge upon the composition of associated species and their capacity to maintain key ecological processes in spite of ongoing disturbances.