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Toward more efficient schemes for achieving deeply degenerate molecular Fermi gases, we study anisotropic thermalization in dilute gases of microwave shielded polar molecular fermions. For collision energies above the threshold regime, we find that thermalization is suppressed due to a strong preference for forward scattering and a reduction in total cross section with energy, significantly reducing the efficiency of evaporative cooling. We perform close-coupling calculations on the effective potential energy surface derived by Deng [] to obtain accurate two-body elastic differential cross sections across a range of collision energies. We use Gaussian process regression to obtain a global representation of the differential cross section over a wide range of collision angles and energies. The route to equilibrium is then analyzed with cross-dimensional rethermalization experiments, quantified by a measure of collisional efficiency toward achieving thermalization. Published by the American Physical Society2024