A set of styrene-ethylene-butylene-styrene triblock copolymer (SEBS) membranes with 10 or 25 wt% divinyl-benzene (DVB) as a crosslinking agent were prepared and validated. Physicochemical characterization revealed suitable hydrolytic and thermal stability of photo-crosslinked membranes containing 25 wt% DVB and post-sulfonated. These compositions were evaluated in H2/O2 single cells, and electrical and proton conductivities were furtherly assessed. The membranes with the milder post-sulfonation showed greater proton conductivity than those with excessive sulfonation. In terms of electrical conductivity, a universal power law was applied, and the values obtained were low enough for being used as polyelectrolytes. At the analyzed temperatures, the charge transport process follows a long-range pathway or vehicular model. Finally, fuel cell performance revealed the best behavior for the membrane with 25 wt% DVB, photo-crosslinked during 30 min and mild sulfonated, with a promising power density of 526 mW·cm−2. Overall, the results obtained highlight the promising fuel cell performance of these cost-effective triblock copolymer-based membranes and indicate that higher sulfonation does not necessarily imply better power density.