Diffractive optics elements have exhibited many novel characteristics through various methods of employing Pancharatnam-Berry, or geometric, phase. One geometric-phase hologram (GPH) subset, consisting of a π-difference binary sampling, shows polarization-independent properties that are not present in the continuous GPH and the dynamic-phase binary analog. Here, we investigate the binary geometric-phase holograms (bin-GPHs) realized with anisotropic liquid crystal (LC) polymers. First, the optical properties of the ideal binary polarization grating are derived and simulated showing 81% cumulative first-order efficiency, polarization-independent diffraction when applying a π-switching scheme, innate odd (m = 2k + 1) diffractive orders, and variable polarization output. After, experimental results of two key bin-GPH elements, the binary polarization grating (Λ = 30μm) and binary geometric-phase lens (f/100), with π-offset regions and a 0.5μm transition pixel are presented. We found that the fabricated non-ideal bin-GPHs exhibit near-maximum theoretical polarization-insensitive diffraction efficiency and tunable polarization outputs. The simple, and scalable, fabrication of the anisotropic bin-GPH provides the potential for implementation within the next-generation near-eye displays for polarization-invariant beam-steering and waveguides.