In most aqueous redox flow batteries (RFBs), ion exchange membranes are used to suppress crossover of redox active species while enabling conductivity of charge carrying ions. Many aqueous RFB chemistries, such as the all-vanadium RFB, involve metal cations dissolved in acid. In such systems, high proton conductivity affords low ohmic resistance from the membrane, but crossover rates are also high. Organic and metalorganic reactants with extreme chemical stability are an emerging direction for the development of RFB electrolytes, and may enable batteries with long calendar life composed of earth-abundant elements. Moreover, the size and charge numbers of these reactants enable much lower crossover than observed for systems like vanadium RFBs. However, the most stable chemistries use neutral or alkaline electrolytes where protons are not abundant enough to carry the ionic current. Currently, this presents a drawback: the incumbent cation exchange membrane, Nafion, exhibits a factor-of-ten lower conductivity of potassium compared to protons. The present work introduces a new membrane cast from sulfonated Diels-Alder poly(phenylene) to enable improved area-specific resistance while suppressing crossover.Nafion contains a perflourinated hydrophobic backbone with intervals of a flexible side chain that terminates in hydrophilic sulfonic acid moieties. This structure of a hydrophobic backbone with hydrophilic side chains is common to most ion exchange membranes. When a membrane with this polymer structure is hydrated and ion exchanged to an alkali metal cation form, the cations promote aggregation of the ionic groups via rearrangement of the flexible side chains, giving a configuration that is not optimal for ion conductivity. In contrast, the new membrane has a sulfonated hydrophilic backbone and external hydrophobic moieties, which we hypothesize prevents the aggregation effects seen in Nafion to enable efficient ion-selective transport. In the present work, we show that the new membrane affords negligible ferricyanide permeability (< 2 × 10−13 cm2/s) and promising area-specific resistances (< 1 Ω cm2) for a variety of cations. The conductivity of the new membrane in 1 M KCl electrolyte is 3.6 mS cm-1, more than double that of Nafion NR212 measured in the same flow battery cell. We demonstrate the use of this membrane in an alkaline organic RFB, with a ferri-/ferrocyanide posolyte and a 4,4’-((9,10-anthraquinone-2,6-diyl)dioxy)dibutyrate (2,6-DBEAQ) negolyte. Three-electrode voltametric methods for post-cycling detection of crossed-over species will be discussed and their sensitivities compared, in an effort to quantify crossover fluxes during cycling and their possible contributions to capacity fade. We conclude that in this flow battery, the new membrane suppresses crossover of both iron hexacyanide and 2,6-DBEAQ to the extent that any crossed over compounds cannot be detected by our methods, and we assign an upper limit of 2 × 10−7 μmol cm−2 s−1 on the possible crossover flux, amounting to a projected < 1 %/year capacity fade from crossover in the lab-scale cell.