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Electric currents carrying a net spin polarization are widely used in spintronics, whereas globally spin-neutral currents are expected to play no role in spin-dependent phenomena. Here we show that, in contrast to this common expectation, spin-independent conductance in compensated antiferromagnets and normal metals can be efficiently exploited in spintronics, provided their magnetic space group symmetry supports a non-spin-degenerate Fermi surface. Due to their momentum-dependent spin polarization, such antiferromagnets can be used as active elements in antiferromagnetic tunnel junctions (AFMTJs) and produce a giant tunneling magnetoresistance (TMR) effect. Using RuO₂as a representative compensated antiferromagnet exhibiting spin-independent conductance along the [001] direction but a non-spin-degenerate Fermi surface, we design a RuO₂/TiO₂/RuO₂(001) AFMTJ, where a globally spin-neutral charge current is controlled by the relative orientation of the Néel vectors of the two RuO₂electrodes, resulting in the TMR effect as large as ~500%. These results are expanded to normal metals which can be used as a counter electrode in AFMTJs with a single antiferromagnetic layer or other elements in spintronic devices. Our work uncovers an unexplored potential of the materials with no global spin polarization for utilizing them in spintronics.