Recently, evidence has emerged for a field-induced even-to odd-parity superconducting phase transition in CeRh2As2 [S. Khim et al., arXiv:2101.09522]. Here we argue that the P 4/nmm non-symmorphic crystal structure of CeRh2As2 plays a central role in enabling this transition. Specifically, the non-symmorphic symmetries enforce an unusual spin structure near Brillouin zone boundaries that ensures large spin-orbit interactions in these regions of momentum space. This enables a high-temperature field-induced even-to odd-parity transition. We further provide an explicit illustration of the robustness of a field induced odd-parity state within a DFT-inspired model of the superconducting state that includes Fermi surfaces located about a Dirac line at the zone boundary and also about the zone center. Finally, we comment on the relevance of our results to superconducting FeSe, which also crystallizes in a P 4/nmm structure.