In optical transitions which involve collisions between photons (from light) and electrons present in a solid, say, the transition rate is typically given by Fermi's golden rule. But the equation doesn't take into account spin of the electron. Is there a qualitative explanation as to why a photon doesn't interact with the spin of an electron?
Photons do interact with electron spin. The famous astronomical 21cm line is an example, as is electron paramagnetic resonance. Magnetic resonance imaging is base on interaction with the proton spin. This is called magnetic dipole interaction. It is described by the Pauli equation in the nonrelativistic limit.
Electric dipole interaction is independent of spin, as it changes only the orbital angular momentum. This is described by the Schrodinger equation in the nonrelativistic limit.