Atomic ordering provides a route to modify local symmetry at fixed composition, but its influence on spin-orbit-coupled (SOC) responses remains difficult to separate from accompanying structural and electronic changes. Here, we use first-principles calculations to examine five Bi/Y occupation patterns in fixed-composition ${\left({\mathrm{Y}}_{0.5}{\mathrm{Bi}}_{0.5}\right)}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$. Reversing the site-order polarity leaves the equilibrium volume, band-gap scale, broadband manifold, and diagonal dielectric response nearly unchanged, while changing the distributions of Fe-centered projected density of states spectral centroids and the $\mathrm{Bi}\text{−}6p/\mathrm{Fe}\text{−}3d$ spectral weight near the conduction edge. The SOC-sensitive observables respond much more strongly: The effective [111]-projected magnetic anisotropy energy (MAE) density $K$ varies approximately linearly with the site-order parameter and changes sign near the occupation-balanced configuration, whereas the off-diagonal dielectric tensor and the resulting Kerr and Faraday spectra change markedly. These results establish site order as a fixed-composition control variable for reversing magnetic anisotropy and reshaping magneto-optical response without substantially altering the average structural or electronic framework.

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• Magnetic anisotropy
• Magneto-optical effect
• Spin-orbit coupling
• Structural order parameter