Innovative nanofibrous membranes based on Pd/Au catalysts immobilized via electrospinning onto different polymers were engineered and tested in the selective oxidation of 5-(hydroxymethyl)furfural in an aqueous phase. The type of polymer and the method used to insert the active phases in the membrane were demonstrated to have a significant effect on catalytic performance. The hydrophilicity and the glass transition temperature of the polymeric component are key factors for producing active and selective materials. Nylon-based membranes loaded with unsupported metal nanoparticles were demonstrated to be more efficient than polyacrylonitrile-based membranes, displaying good stability and leading to high yield in 2,5-furandicarboxylic acid. These results underline the promising potential of large-scale applications of electrospinning for the preparation of catalytic nanofibrous membranes to be used in processes for the conversion of renewable molecules.