We present the spin-orbit (SO) and Renner-Teller (RT) quantum dynamics of the spin-forbidden quenching O((1)D) + N(2)(X(1)Σ(g)(+)) → O((3)P) + N(2)(X(1)Σ(g)(+)) on the N(2)O X(1)A', ã(3)A", and b(3)A' coupled PESs. We use the permutation-inversion symmetry, propagate coupled-channel (CC) real wavepackets, and compute initial-state-resolved probabilities and cross sections σ(j(0)) for the ground vibrational and the first two rotational states of N(2), j(0) = 0 and 1. Labeling symmetry angular states by j and K, we report selection rules for j and for the minimum K value associated with any electronic state, showing that ã(3)A" is uncoupled in the centrifugal-sudden (CS) approximation at j(0) = 0. The dynamics is resonance-dominated, the probabilities are larger at low K, σ(j(0)) decrease with the collision energy and increase with j(0), and the CS σ(0) is lower than the CC one. The nonadiabatic interactions play different roles on the quenching dynamics, because the X(1)A'-b(3)A' SO effects are those most important while the ã(3)A"-b(3)A' RT ones are negligible.