By "take the SE seriously," you mean wave function realism, right (so-called "psi-ontologists")? The wave function and therefore the SE is still very meaningful for psi-epistemologists (like me), it's just not considered part of objective reality.Perhaps, but I would say that such approaches do not take the Schrodinger equation seriously. If the wave function describes only a subjective knowledge of an agent, then all the stuff about which the agent knows nothing (and there is certainly a lot of such stuff) is not described by the Schrodinger equation. In fact it is not described by anything, because in subjective approaches the agent cannot describe something that he does not have a knowledge about. The wave function of the Universe, which makes sense in approaches (like BM and MWI) in which the Schrodinger equation is taken seriously, does not make any sense in subjective approaches.
Is there a wave function of the Moon when the agent knows nothing about the Moon? Subjective approaches say no, other approaches say yes.