I think there's an ambiguity between "realism" in the sense of "these statements I'm making are answers to a well-formed question and have a truth value" and "morality is a transcendent ineffable stuff floating out there which compels all agents to obey and could make murder right by having a different state".

Yes -- and the important thing to remember is that the second view, which all of us here agree is silly, is the naive, common-sense human view. It's what people are automatically going to think you're talking about if you go around shouting "Yes Virginia, there are moral facts after all!"

Meanwhile, the general public has a term for the view that you and I share: they call it "moral relativism".

I don't recall exactly, and I haven't yet bothered to look it up, but I believe when you first introduced your metaethics, there were people (myself among them, I think), who objected, not to your actual meta-ethical views, but to the way that you vigorously denied that you were a "relativist"; and you misunderstood them/us as objecting to your theory itself (I think you maybe even threw in an accusation of not comprehending the logical subtleties of Loeb's Theorem).

What makes the theory relativist is simply the fact that it refers explicitly to particular agents -- humans. Thus, it is automatically subject to the "chauvinism" objection with respect to e.g. Babyeaters: we prefer one thing, they prefer another -- why should we do what we prefer rather than what they prefer? The correct answer is, of course, "because that's what we prefer". But people find that answer unpalatable -- and one reason they might is because it would seem to imply that different human cultures should similarly run right over each other if they don't think they share the same values. Now, we may not like the term "relativism", but it seems to me that this "chauvinism" objection is one that you (and I) need to take at least somewhat seriously.