There's broadly two areas where MWI has ethical implications. One is over the fact that MW means low poibability events have to happen very time -- as opposed to single universe physics, where they usually don't. The other is over whether they are discounted in moral significance for being low in quantum mechanical measure or probability
It can be argue that probability calculations come out the same under different interpretations of QM, but ethics is different. The difference stems from the fact that what what other people experience is relevant to them, wheareas for a probability calculation, I only need to be able to statistically predict my own observations. Using QM to predict my own observations, I can ignore the question of whether something has a ten percent chance of happening in the one and only world, or a certainty of happening in one tenth of possible worlds.
You can have objective information about observations, and if your probability calculus is wrong , you will get wrong results and know that you are getting wrong results. That is the negative feedback that allows physics to be less wrong.
You can have subjective information about your own mental states, and if your personal calculus is wrong , you will get wrong results and know that you are getting wrong results. That is the negative feedback that allows personal decision theory to be less wrong.
Altruistic ethics is different. You don't have either kind of direct evidence, because you are concerned with other people's subjective sensations , not objective evidence , or your own subjectivity. Questions about ethics are downstream of questions about qualia, and qualia are subjective, and because they are subjective, there is no reason to expect them to behave like third person observations.
We have to infer that someone else is suffering , and how much, using background assumptions. For instance, I assume that if you hit your thumb with a hammer , it hurts you like it hurts me when I hit my thumb with a hammer.
One can have a set of ethical axioms saying that I should avoid causing death and suffering to others, but to apply them under many worlds assumptions, I need to be able to calculate how much death and suffering my choices cause in relation to the measure. Which means I need to know whether the measure or probability of a world makes a difference to the intensity of subjective experience.. including the option of "not at all", and I need to know whether the deaths of then people in a one tenth measure world count as ten deaths or one death.
Suppose they are discounted.
If people in low measure worlds experience their suffering fully, then a 1%, of creating a hell-world would be equivalent in suffering to a 100% chance. But if people in low measure worlds are like philosophical zombies, with little or no phenomenal consciousness, so that their sensations are faint or nonexistent, the moral hazard is much lower.
A similar, but slightly less obvious argument applies to causing death. Causing the "death" of a complete zombie is presumably as morally culpable as causing the death of a character in a video game...which, by common consent, is not problem at all. So... causing the death of a 50% zombie would be only half as bad as killing a real person...maybe.
There is an alternative way of cashing out quantum mechanical measure due to David Deutsch. He supposes that you can have exact duplicates of worlds , which form sets of identical worlds, and which have no measure of their own. Each set contains different worlds, making the sets unique, each world within a set is identical to the others. Counting the worlds in an equivalence set gives you the equivalent of measure.
Under this interpretation, you should ethically discount low-measure worlds (world sets) because there are fewer people in them.
The approach where suffering and moral worth are discounted according to measure has the convenient property that it works like probability theory, so that you don't have to take an interpretation of QM into account. But , if you are arguing to the conclusion that the interpretation of QM is ethically neutral, you can't inject the same claim as an assumption, without incurring circularity.
What's needed is a way of deciding the issue of measure versus reality versus consciousness ethical value that is not question begging. We are not going to get a rigourous theory based on physics alone, because physics does not explicitly deal with reality, consciousness or ethical value. But there are some hints. One important consideration is that under many world's theory, all worlds must have measures summing to 1, so any individual world,including ours, has measure less than 1. But our world and our consciousness seem fully real to us; if there is nothing special about our world, then the inhabitants of other worlds presumably feel the same. And that is just the premise that leads to the conclusion that many world's theory does impact ethics.
Of course , there is also the metaphysical issue rhat MW is a deterministic theory, so there is a question about whether we can chos to behave differently at all. But MW is not the only deterministic theory...newtonian physics had the same problem