Oxygen vacancies play a crucial role in the control of the electronic, magnetic, ionic, and transport properties of functional oxide perovskites. Rare earth nickelates (RENiO$_{3-x}$) have emerged over the years as a rich platform to study the interplay between the lattice, the electronic structure, and ordered magnetism. In this study, we investigate the evolution of the electronic and magnetic structure in thin films of RENiO$_{3-x}$, using a combination of X-ray absorption spectroscopy and imaging, resonant X-ray scattering, and extended multiplet ligand field theory modeling. We find that oxygen vacancies modify the electronic configuration within the Ni-O orbital manifolds, leading to a dramatic evolution of long-range electronic transport pathways despite the absence of nanoscale phase separation. Remarkably, magnetism is robust to substantial levels of carrier doping, and only a moderate weakening of the $(1/4, 1/4, 1/4)_{pc}$ antiferromagnetic order parameter is observed, whereas the magnetic transition temperature is largely unchanged. Only at a certain point long-range magnetism is abruptly erased without an accompanying structural transition. We propose the progressive disruption of the 3D magnetic superexchange pathways upon introduction of point defects as the mechanism behind the sudden collapse of magnetic order in oxygen-deficient nickelates. Our work demonstrates that, unlike most other oxides, ordered magnetism in RENiO$_{3-x}$ is mostly insensitive to carrier doping. The sudden collapse of ordered magnetism upon oxygen removal may provide a new mechanism for solid-state magneto-ionic switching and new applications in antiferromagnetic spintronics.