Membranes with fast and selective transport of protons and cations are required for a wide range of electrochemical energy conversion and storage devices, such as proton‐exchange membrane (PEM) fuel cells and redox flow batteries. Here we report a new approach to designing solution‐processable ion‐selective polymer membranes with both intrinsic microporosity and ion‐conductive functionality. This was achieved by synthesizing polymers with rigid and contorted backbones, which incorporate hydrophobic fluorinated and hydrophilic sulfonic acid functional groups, to produce membranes with negatively‐charged subnanometer‐sized confined ionic channels. The facilitated transport of protons and cations through these membranes, as well as high selectivity towards nanometer‐sized redox‐active molecules, enable efficient and stable operation of an aqueous alkaline quinone redox flow battery and a hydrogen PEM fuel cell. This membrane design strategy paves the way for producing a new‐generation of ion‐exchange membranes for electrochemical energy conversion and storage applications.