Ion exchange membranes (IEMs) are a key component of electrochemical processes that purify water, generate clean energy, and treat waste. Most conventional polymer IEMs are covalently cross-linked, which results in a challenging tradeoff relationship between two desirable properties─high permselectivity and high conductivity─in which one property cannot be changed without negatively affecting the other. In an attempt to overcome this limitation, in this work we synthesized a series of anion exchange membranes containing non-covalent cross-links formed by a hydrogen bond donor (methacrylic acid) and a hydrogen bond acceptor (dimethylacrylamide). We show that these monomers act synergistically to improve both membrane permselectivity and conductivity relative to a control membrane without non-covalent cross-links. Furthermore, we show that the hydrogen bond donor and acceptor loading can be used to tune permselectivity and conductivity relatively independently of one another, escaping the tradeoff observed in conventional membranes.