A fundamental challenge in ecology continues to be identifying mechanisms that stabilize community dynamics. In recent years, there has been growing empirical evidence highlighting that eco-evolutionary feedbacks can dramatically impact community-level properties, including stability. Moreover, there is evidence that evolution happens at rates ranging from slower than to commensurate to ecological rates, and this affects the impact of feedbacks. Theoretical work to mechanistically understand how eco-evolutionary feedbacks impact stability has focused on specific ecological modules with just one or two evolving species. Here, we provide a general framework for determining the effects of eco-evolutionary feedbacks on stability in communities with an arbitrary number of interacting species and evolving traits for when evolution is slow and fast. We characterize how these feedbacks lead to stable communities that would be unstable in the absence of the feedbacks, and vice versa. In addition, we show how this characterization provides a partitioning of the roles of direct and indirect feedbacks between ecological and evolutionary processes on community stability, and how this partitioning depends on the rate of evolution relative to ecology. Applying our methods to models of competing species and food chains, we demonstrate how the functional form of trade-offs, genetic correlations between traits, and the rate of evolution determine whether eco-evolutionary feedbacks stabilize or destabilize community dynamics.