Clonal microbes can switch between different phenotypes and recent theoretical work has shown that stochastic switching between these subpopulations can stabilize microbial communities. This phenotypic switching need not be stochastic, however, but can also be in response to environmental factors, both biotic and abiotic. Here, motivated by the bacterial persistence phenotype, we explore the ecological effects of such responsive switching by analyzing phenotypic switching in response to competing species. We show how the stability of microbial communities with responsive switching differs generically from that of communities with stochastic switching only. To understand this effect, we go on to analyse simple two-species models. Combining exact results and numerical simulations, we extend the classical stability results for models of two competing species without phenotypic variation to the case where one of the two species switches, stochastically and responsively, between two phenotypes. In particular, we show that responsive switching can stabilize coexistence even when stochastic switching on its own does not affect the stability of the community.