The spin transport equations for polarized deuterium-tritium (DT) fusion plasma are derived with the density matrix formulation, which are used to investigate the hydrodynamics of polarized DT-gas-filled targets during indirectly driven inertial confinement fusion implosions. The depolarization of DT ions by strong self-generated magnetic fields can be captured by the spin transport equation. The neutron yield, angular distribution and neutron beam polarization are obtained from three-dimensional spin transport hydrodynamics simulations of the target implosions. The simulation results indicate that an optimized spin alignment of the polarized target can reduce the depolarization of DT ions and the neutron beams induced by polar mode asymmetries in indirectly driven implosions.