Polymeric membranes are widely used for salt removal, but mechanism of ion permeation is still insufficiently understood. Here we analyze ion transport in polymers relevant to desalination, dense aromatic polyamide Nomex and cellulose acetate (CA), using impedance spectroscopy, focusing on the effects of the salt type, concentration and pH. The results highlight the role of proton uptake in ion permeation. For Nomex the exceptionally high affinity to proton results in a power-low scaling of conductivity with salt concentrations with an unusual exponent 1/2. The results for CA suggest dominance of pore transport, with pore charge increasing with decreasing pH, which contradicts previous view of CA as a weakly acidic polymer and points to proton uptake as possible pore charging mechanism. The observed effects may have far-reaching consequences in desalination, as even at neutral pH they may both enhance and suppress salt permeation and affect pH changes.