Conserving angular momentum in elementary decay/reaction

I think what's going on here is two things: (1) the forbidden processes, unlike the one in your example, involve either a single particle in the initial state or a single particle in the final state; and (2) there is a hidden assumption that we're dealing with pointlike particles and interactions that happen at a pointlike vertex.

A simple example is a particle of spin 0 decaying to a spin 0 plus a spin 1. We can get into a frame in which the initial particle is at rest at the origin. Then because the particles are pointlike and decay occurs at a pointlike vertex, each of the final particles has zero orbital angular momentum in the final state. This process is therefore forbidden.

There is then the question of why the above argument still holds for an example like photon emission by an excited spin-0 state of hydrogen, decaying to the ground state, which is indeed forbidden. (It goes only by two-photon emission.) The hydrogen atom is not pointlike, it's composite. I'm tempted to say that it still works because angular momentum has to be conserved at that vertex, which doesn't include the proton, but that may be wrong. We do, after all, have to have a proton present for this decay to happen -- a free electron can't gamma decay.