Straight dark solitons in two-dimensional (2D) quantum fluids usually decay by transverse modulational instability, with no intrinsic suppression in contact-interacting Bose–Einstein condensates (BECs). We theoretically show that anisotropic long-range interactions in a quasi-2D dipolar BEC stabilize an embedded straight soliton, with spontaneous stripe order providing stronger pinning. The excitation spectra show that the lowest transverse solitonic branch remains gapped, while stripe-supersolid density modulation further hardens this branch and increases the soliton bending stiffness, penalizing transverse deformation. Accessible in current ${}^{166}$Er and ${}^{164}$Dy platforms, these results establish interaction-driven protection for straight dark solitons in structured quantum fluids.