Earlier quoted context omitted.
Abstractions need not be approximations. Schroedinger's equation is an abstraction, but as far as we know it's exact.
Schrodinger's equation doesn't even include special relativistic effects. It's not exact (at least not if you mean it exactly describes nature in general). Neither is Dirac's equation; it includes special relativistic effects for a single particle, but not general relativistic effects or multi-particle interactions (at least as far as I understand it).
The general form using the unspecified Hamiltonian operator is compatible with relativity.