Symmetry constraints are built into a semiclassical propagation scheme. It is then applied to treat H+Ne-2 collisions at 30 K, where quantum selection rules restrict the final rotational states of symmetric Ne-2 molecules to the even manifold. The cross sections for state-to-state transitions are calculated for symmetric and nonsymmetric isotopic compositions of Ne-2. All bound and long-lived quasibound (trapped behind the centrifugal barrier) states of Ne-2 are considered. This semiclassical method captures symmetry effects and shows satisfactory agreement with the quantum results.