Multiple anthropogenic impacts, including bleaching from climate change-related thermal stress, threaten coral reefs. Protecting coral capacity to respond to the increase in future thermal stress expected with climate change can involve (1) protecting coral reefs with characteristics indicative of greater resistance and resilience to climate change, and (2) reducing other anthropogenic impacts that are more likely to reduce coral resistance and resilience to climate change. Here, we quantitatively compare possible priorities and existing recommendations for protecting coral response capacity to climate change. Specifically, we explore the relative importance of the relevant dynamics, processes, and parameters in a size-structured model of coral and zooxanthellae ecological and evolutionary dynamics given projected future thermal stress. Model results with varying initial conditions indicate that protecting diverse coral communities is critical, and protecting communities with higher abundances of more thermally tolerant coral species and symbiont types secondary, to the long-term maintenance of coral cover. A sensitivity analysis of the coral population size in each size class and the total coral cover with respect to all parameter values suggests greater relative importance of reducing additional anthropogenic impacts that affect coral–macroalgal competition, early coral life history stages, and coral survivorship (compared with reproduction, growth, and shrinkage). Finally, model results with temperature trajectories from different locations, with and without connectivity, indicate that protection of, and connectivity to, low-thermal-stress locations may enhance the capacity for corals to respond to climate change.