We investigate the pressure-dependent magnetism of the quasi-one-dimensional solid solution Ca1-xNaxCr2O4 using neutron diffraction, Cr K-edge x-ray absorption spectroscopy, and muon spin rotation/relaxation. Na substitution is known to increase oxygen-ligand hole density (partial Cr3+ to Cr4+ character) and to drive the evolution from incommensurate order in CaCr2O4 to commensurate antiferromagnetism in NaCr2O4, suggesting a complex interplay between charge doping and structural changes. Here we apply hydrostatic pressure to tune the lattice without altering the nominal hole count, thereby separating compression effects from ligand-hole physics. For x = 0 and x = 0.5 the magnetic transition temperature is essentially pressure independent within our explored range, whereas in NaCr2O4 long-range order is progressively suppressed with pressure, as seen by a decrease of TN and of the magnetic Bragg intensity. Over the same pressure range, Cr K-edge x-ray absorption spectroscopy shows no resolvable change in the average Cr valence or coordination, and the refined corner-sharing Cr–O–Cr geometry remains nearly invariant within uncertainty. Extrapolating the pressure dependence of the magnetic order parameter suggests a critical pressure Pc = 107(8) kbar for complete suppression of long-range order. These results support ligand-hole density as the primary control parameter across Ca1-xNaxCr2O4, with pressure acting as a secondary electronic tuning knob that weakens ordering in the Na-rich end member without inducing a new magnetic phase.