I think there's an ambiguity between "realism" in the sense of "these statements I'm making about 'what's right' are answers to a well-formed question and have a truth value" and "the subject matter of moral discourse is a transcendent ineffable stuff floating out there which compels all agents to obey and which could make murder right by having a different state". Thinking that moral statements have a truth value is cognitivism, which sounds much less ambiguous to me, and that's why I prefer to talk about moral cognitivism rather than moral realism.
As a moral cognitivist, I would look at your diagram and disagree that the Baby-Eating Aliens and humans have different views of the same subject matter, rather, we and they are talking about a different subject matter and it is an error of the computer translation programs that the word comes out as "morality" in both cases. Morality is about how to save babies, not eat them, everyone knows that and they happen to be right. If we could get past difficulties of the translation, the babyeaters would agree with us about what is moral, we would agree with them about what is babyeating, and we would agree about the physical fact that we find different sorts of logical facts to be compelling.
I have a pending post-to-write on how, to the best of my knowledge, there are only two sorts of things that can make a proposition "true", namely physical events and logical implications, and of course mixtures of the two. I mention this because we have a legitimate epistemic preference for simpler hypotheses about the causes of physical events, but no such thing as an epistemic preference for "simpler axioms" when we are talking about logical facts. We may have an aesthetic preference for simpler axioms in math, but that is not the same thing. If there's no preference for simpler assumptions, that doesn't mean the issue is not a factual one, but it may suggest that we are dealing with logical facts rather than physical facts (statements which are made true by which conclusions follow from which premises, rather than the state of a causal event).
Added: Since I have a definite criterion for something being a "fact", I defend the notion of fact-ness against the charge of being a floating extra.
Morality is about how to save babies, not eat them, everyone knows that and they happen to be right. If we could get past difficulties of the translation, the babyeaters would agree with us about what is moral, we would agree with them about what is babyeating, and we would agree about the physical fact that we find different sorts of logical facts to be compelling.
This simply pushes the problem back one level, by making the word "morality" descriptive instead of normative. Morality is X and babyeating is Y. But how should one choose between morality and babyeating? Now, instead of a moral anti-realist, I'm a moral realist, a babyeating realist, and normative judgement anti-realist.
On Wei_Dai's complexity of values post, Toby Ord writes:
The kind of moral realist positions that apply Occam's razor to moral beliefs are a lot more extreme than most philosophers in the cited survey would sign up to, methinks. One such position that I used to have some degree of belief in is:
Strong Moral Realism: All (or perhaps just almost all) beings, human, alien or AI, when given sufficient computing power and the ability to learn science and get an accurate map-territory morphism, will agree on what physical state the universe ought to be transformed into, and therefore they will assist you in transforming it into this state.
But most modern philosophers who call themselves "realists" don't mean anything nearly this strong. They mean that that there are moral "facts", for varying definitions of "fact" that typically fade away into meaninglessness on closer examination, and actually make the same empirical predictions as antirealism.
Suppose you take up Eliezer's "realist" position. Arrangements of spacetime, matter and energy can be "good" in the sense that Eliezer has a "long-list" style definition of goodness up his sleeve, one that decides even contested object-level moral questions like whether abortion should be allowed or not, and then tests any arrangement of spacetime, matter and energy and notes to what extent it fits the criteria in Eliezer's long list, and then decrees goodness or not (possibly with a scalar rather than binary value).
This kind of "moral realism" behaves, to all extents and purposes, like antirealism.
I might compare the situation to Eliezer's blegg post: it may be that moral philosophers have a mental category for "fact" that seems to be allowed to have a value even once all of the empirically grounded surrounding concepts have been fixed. These might be concepts such as "would aliens also think this thing?", "Can it be discovered by an independent agent who hasn't communicated with you?", "Do we apply Occam's razor?", etc.
Moral beliefs might work better when they have a Grand Badge Of Authority attached to them. Once all the empirically falsifiable candidates for the Grand Badge Of Authority have been falsified, the only one left is the ungrounded category marker itself, and some people like to stick this on their object level morals and call themselves "realists".
Personally, I prefer to call a spade a spade, but I don't want to get into an argument about the value of an ungrounded category marker. Suffice it to say that for any practical matter, the only parts of the map we should argue about are parts that map-onto a part of the territory.