Recent developments in photonic topological phases have revealed that protected edge modes can emerge not only from global topological invariants, but also from symmetry-enforced polarization mismatches between distinct bulk phases. In this work, we investigate the capabilities and limitations of a square-lattice (C₄-symmetric) photonic crystal (PC) composed of a single dielectric material that supports interface-localized modes at the boundary between regions characterized by distinct obstructed atomic limits (OALs). These modes are confined to a common band gap and exhibit high transmission, even in the presence of structural perturbations. Our analysis reveals that the interface modes are stabilized by a mismatch in the position of Wannier centers between the two adjoining crystals. We demonstrate nearly lossless transmission around sharp turns and through localized defects, though the robustness depends asymmetrically on the side of perturbation, reflecting the partial nature of the protection. We also show that increasing the number of PC periods surrounding the interface enhances both modal confinement and spectral stability. These findings establish polarization mismatch between OALs as a practical and fabrication-compatible mechanism for engineering robust photonic transport in C₄-symmetric systems.