The geometric and dynamic phases have competing effects as far as the scattering of light from an inhomogeneous anisotropic optical medium is concerned. If fine-tuned appropriately, these effects can completely cancel each other for a chosen spin component while having an additive effect on the orthogonal component. Here, we show a manifestation of extraordinary spin-selective modes in the Fourier spectrum of a Gaussian beam transmitted through an anisotropic disordered medium. We realize the concept by using a twisted nematic liquid-crystal-based spatial light modulator with random gray-level distributions for an incident Gaussian beam.