Spatial variations in magnetic anisotropy impede the spin-orbit-torque-driven motion of chiral domain walls in perpendicularly magnetized nanowires. We show that the local geometry of a two-dimensional anisotropy landscape can select which wall polarity propagates under a given current. Micromagnetic simulations of spatially correlated random anisotropy landscapes generated by diffusion-based smoothing reveal different propagation outcomes for up–down and down–up walls within the same disorder realization. A single inclined anisotropy boundary isolates the mechanism: in the presence of the Dzyaloshinskii–Moriya interaction, opposite wall polarities develop opposite current-induced tilts, producing different alignment with the boundary and hence different pinning strengths. Reversing the boundary inclination interchanges the pinned and propagating polarities. An extended collective-coordinate model captures this geometric selection and distinguishes the propagation threshold from the static pinning limit.