While previous studies on character displacement tended to focus on trait divergence and convergence as a result of long-term evolution, recent studies suggest that character displacement can be a special case of evolutionary rescue, where rapid evolution prevents species extinction by weakening interspecific competition. Here we analyzed a simple model to examine how the magnitude of genetic variation affects evolutionary rescue via ecological and reproductive character displacement that weakens interspecific competition in exploitation of shared resources (i.e., resource competition) and in the mating process caused by incomplete species recognition (i.e., reproductive interference), respectively. We found that slow trait divergence due to small genetic variance results in species extinction in reproductive character displacement but not in ecological character displacement. This is because one species becomes rare in slow character displacement, and this causes deterministic extinction due to minority disadvantage of reproductive interference. On the other hand, there is no deterministic extinction in the process of ecological character displacement. Furthermore, species extinction becomes less likely in the case of positive covariance between ecological and reproductive traits as divergence of the ecological trait (e.g., root depths) increases the divergence speed of the reproductive trait (e.g., flower colors) and vice versa. It will be interesting to compare intraspecific genetic (co)variance of ecological and reproductive traits in future studies for understanding how ecological and reproductive character displacement occur without extinction.