Ever since the discovery of neutrinos, one question has daunted us, are neutrinos their own antiparticles? One remarkable possibility is that neutrinos have a pseudo-Dirac nature, truly Majorana neutrinos which behave, for all practical purposes, as Dirac fermions, only distinguishable by tiny mass-squared differences. Such mass differences would induce oscillations that could only be conspicuous over astrophysical baselines. We analyze the neutrino data from SN1987A in the light of these active-sterile oscillations and find a mild preference () for a non-zero quadratic mass difference . Notably, the same data is able to exclude with , the tiniest mass differences constrained so far. We further consider the future sensitivity of next-generation experiments like the Deep Underground Neutrino Experiment (DUNE) and Hyper-Kamiokande (HK) and demonstrate that, for a future galactic SN occurring at , mass-squared differences as small as could be explored.