Selective ion transport across membranes is critical to the performance of many electrochemical energy storage devices. While design strategies enabling ion-selective transport are well-established, enhancements in membrane selectivity are made at the expense of ionic conductivity. To design membranes with both high selectivity and high ionic conductivity, there are cues to follow from biological systems, where regulated transport of ions across membranes is achieved by transmembrane proteins. The transport functions of these proteins are sensitive to their environment: physical or chemical perturbations to that environment are met with an adaptive response. Here we advance an analogous strategy for achieving adaptive ion transport in microporous polymer membranes. Along the polymer backbone are placed redox-active switches that are activated in situ, at a prescribed electrochemical potential, by the device's active materials when they enter the membrane's pore. This transformation has little influence on the membrane's ionic conductivity; however, the active-material blocking ability of the membrane is enhanced. We show that when used in lithium-sulfur batteries, these membranes offer markedly improved capacity, efficiency, and cycle-life by sequestering polysulfides in the cathode. The origins and implications of this behavior are explored in detail and point to new opportunities for responsive membranes in battery technology development.