Does ones interpretation of quantum mechanics alter one's moral philosophy?
You have at play the intersection of physical theory and ethical theory, each distinctive and large projects. Your question asks after how presumptions about physicalism affect one's theory of right and wrong action. This is clearly a metaphysical issue insofar as it touches upon a host issues related to how theories themselves relate. From the philosophy of science, let us introduce the idea of theory-ladenness. From WP:
Semantic theory-ladenness refers to the impact of theoretical assumptions on the meaning of observational terms while perceptual theory-ladenness refers to their impact on the perceptual experience itself. Theory-ladenness is also relevant for measurement outcomes: the data thus acquired may be said to be theory-laden since it is meaningless by itself unless interpreted as the outcome of the measurement processes involved.
Insofar as science is a form of empiricism, and a moral theory has empirical presumptions, then the answer to your question is absolutely, ones interpretation of quantum mechanics can alter one's philosophy. That is because ethics in a very real sense is about formulating normative statements about action in the physical world. That even applies to a misunderstanding of physical theory. Let's take a Schrödinger's cat as a moral dilemma.
A simplistic and (IMNSHO) wrong interpretation is to believe in the claim that the cat is alive and dead at the same time in the vein of scientific realism. Suspending the logical challenge of accepting such a situation (a scientific instrumentalist need not grapple with such an ontological contradiction), one now has a very real moral dilemma. Is it okay to run an experiment putting a cat in a box to see what happens? We now have two possible theoretical presuppositions: the realist case and the instrumentalist case. Let's see the outcome.
Realist case: By conducting the experiment, you are killing exactly 1 cat. So, if anyone is pondering the ethics of such an experiment, and one rejects the act of killing a cat under these circumstances immoral, then clearly the experiment is immoral. Thus, some disciple of Peter Singer may outline quite the sophisticated and persuasive argument based on an interpretation of quantum mechanics to arrive at the conclusion such an experiment is unethical.
Instrumentalist case: An instrumentalist would say that the logical contradiction to having an unobserved cat alive and dead simultaneously has nothing to do with physical reality at all. In fact, such an experiment with a detector cannot be realized for this or that reason, and putting the cat in the box, covering him, and executing the protocol results in the limits of our theorization in predicting outcomes. Hence, the cat being alive and dead is a conceptual reality, not a physical one. Thus, since no cats can possibly die in such an experiment, the cat will remain unharmed, and no unethical action has occurred.
So, who is right? Well, to the extent you agree with one ethical argument or the other is going to be a function of both your views on physical and ethical theory combined, with the former determining the outcome of the latter!