We study experimentally and numerically the influence of orthogonal optical feedback on the polarization-resolved light versus bias current characteristic ( $L–I$ curve) of vertical-cavity surface-emitting lasers (VCSELs). The feedback scheme is such that only one linear polarization is selected to be fed back into the laser while the orthogonal polarization is completely suppressed before the output is rotated $90°$ and reinjected into the laser. We experimentally demonstrate that weak feedback levels modify the polarization switching point only slightly, but as the feedback increases the otherwise depressed mode grows and the hysteresis is suppressed. While polarization-preserved and X-orthogonal feedback have similar effects (X indicates the direction of the polarization selected at threshold), Y-orthogonal feedback strongly modifies the shape of the $L–I$ curve, even suppressing the polarization-switching for strong enough feedback. Numerical simulations of the spin-flip model show good qualitative agreement with the observations. We also analyze the influence of various parameters, such as linear birefringence, dichroism, and the spin-flip relaxation rate.