Chiral spacer cations crystallize two-dimensional hybrid perovskites in the polar Sohncke group P2₁, which places the polar axis in the inorganic layer. We analyze the spin-orbit field that this geometry allows and test it against first-principles spin textures of ten polar chiral lead-halide perovskites, their mirror enantiomers and four halide-substituted analogues. The point group C₂ with the twofold axis in the layer forbids the helical Rashba field and allows a linear term γ₁ kₓ σ_z, the Rashba interaction of the in-plane polar axis, together with chirality-related Dresselhaus and radial terms. Thirty-four two-band k · p models were fitted to each band pair and ranked by the agreement of their spin directions with the calculation rather than by the band energies, which cannot distinguish them. In all strongly polar compounds, the conduction band is described by the persistent term alone, with γ₁ = 1.09-1.98 eV Å and a spin agreement of at least 0.98, whereas the best Rashba or Dresselhaus model reaches 0.20. The R and S enantiomers of each compound have opposite polarizations, and therefore opposite γ₁ and opposite persistent spin textures of equal magnitude, as required by the mirror that relates them; this holds in all ten compounds, so the choice of the enantiomer selects the spin direction. The magnitude of γ₁ correlates with the disparity of the in-plane Pb-X-Pb angles (r = 0.95). With electron masses of 0.26-0.43 mₑ along the spin-splitting directions, the associated persistent spin helices have wavelengths of 3.4-8.2 nm.