Topological metals are a new class of materials that feature Fermionic quasiparticles with the presence of non-trivial band crossings near the Fermi level. In this work, we focus on establishing crystal structure ground states and the corresponding topological properties of MnRhP. Under ambient pressure and low temperatures, we find that an orthorhombic oP12 polymorph is favored over the known hexagonal hP9 phase. Pressures above 15 GPa stabilize tetragonal (tP6′), hexagonal (hP9′), and orthorhombic (oP12′) phases with inverted population of metal sites. While oP12′ has the lowest enthalpy, we show that hP9′ is more consistent with the previous X-ray diffraction data collected at 60 GPa. Our analysis of hP9 and oP12 topological properties reveals the existence of nodal lines around the Δ-point that are gapped out when spin-orbit coupling effects are included and transform into Weyl nodes with opposite chirality near the Fermi level. The calculated large values of the anomalous Hall conductivity in hP9, oP12, and tP6′ and the Z2 topological invariant in the non-magnetic hP9′ can be used to verify the predicted non-trivial robust topological features of MnRhP under ambient and high pressures. © 2022 American Chemical Society.