Depolarizing collisions are elastic or quasielastic collisions that equalize the populations and destroy the coherence between the magnetic sublevels of atomic levels. In astrophysical plasmas, the main depolarizing collider is neutral hydrogen. We consider depolarizing rates on the lowest levels of neutral and singly ionized alkali earths Mg I, Sr I, Ba I, Mg II, Ca II, and Ba II, due to collisions with H°. We compute ab initio potential curves of the atom-H° system and solve the quantum mechanical dynamics. From the scattering amplitudes, we calculate the depolarizing rates for Maxwellian distributions of colliders at temperatures T <= 10,000 K. A comparative analysis of our results and previous calculations in the literature is completed. We discuss the effect of these rates on the formation of scattering polarization patterns of resonant lines of alkali earths in the solar atmosphere, and their effect on Hanle effect diagnostics of solar magnetic fields.