On the Copenhagen interpretation, observation collapses quantum states. If panpsychism is true, there are constant observations even at the microscopic level. But it seems inconsistent with our empirical data to suppose constant collapse at the microscopic level. So if we are right to accept the Copenhagen interpretation, we should reject panpsychism.
I suppose one could get out of this by saying that only sapient observation collapses things. But that would be weird indeed. It would mean that the conscious states of infants and dogs are utterly different from ours, because while we observe only collapsed states, they would have the dubious privilege of having superposed observational states.
Instead of the Copenhagen interpretation, we might be able to run this argument against panpsychism from the plausible postulate that it is impossible for there to be superposed states of consciousness conjoined with physicalism. For by physicalism, conscious states will be physical states. Plausibly, if panpsychism is true, the conscious states of fundamental particles will vary depending on the state of the particle, or at least the identity of the particle. But then superpositions of microstates will result in superpositions of conscious states, if conscious states are phsycial states. But superpositions of conscious states are impossible, we have supposed.
Who cares? After all, panpsychism is crazy!
Well, it may be crazy, but it could also be that physicalism leads to panpsychism. And if so, then an argument against panpsychism would provide an argument against physicalism.