The SEP doesn't say this.
Yes, it does. But it says it in the article Moral Anti-Realism, not the article cited above, Moral Realism. The former article is very interested in objectivity constraints, but expresses a great deal of confusion about how to make sense of them; the latter article mentions them only to toss them out for being too confused. (It would not be too surprising if this has something to do with the latter author being more convinced of the truth of 'realism', hence wanting to make the Realism brand simple, clean, and appealing to a wider audience.)
If your encyclopedia has an 'Apples' article and a 'Non-Apples' article, and the two articles completely disagree about what it means to be an 'Apple', then you have your first clue that the word 'Apple' should always come pre-tabooed.
(ETA: More generally, be aware that 'the SEP says X' is less reliable than 'SEP article Y says X', because articles may disagree with each other. SEP is an anthology of introductory essays. We wouldn't normally say 'Very Short Introductions says X', even if we trust the VSI brand quite a bit.)
What the SEP actually says is, "Moral realists are those who think that, in these respects, things should be taken at face value—moral claims do purport to report facts and are true if they get the facts right," and that's it.
Almost. Moral realists (even on the more inclusive definitions) also demand that at least one moral claim of this sort be true. (This is asserted in the sentence right after your quotation terminates.) That's why error theory is not a form of moral realism; realism is a (perhaps improper) subset of success theory.
Oh my god, the "moral anti-realism" article has what is possibly the best opening paragraph I've seen in the SEP:
...It might be expected that it would suffice for the entry for “moral anti-realism” to contain only some links to other entries in this encyclopedia. It could contain a link to “moral realism” and stipulate the negation of the view there described. Alternatively, it could have links to the entries “anti-realism” and “morality” and could stipulate the conjunction of the materials contained therein. The fact that neither of these approac
Continuing my quest to untangle people's confusions about Eliezer's metaethics... I've started to wonder if maybe some people have the intuition that the orthogonality thesis is at odds with moral realism.
I personally have a very hard time seeing why anyone would think that, perhaps in part because of my experience in philosophy of religion. Theistic apologists would love to be able to say, "moral realism, therefore a sufficiently intelligent being would also be good." It would help patch some obvious holes in their arguments and help them respond to things like Stephen Law's Evil God Challenge. But they mostly don't even try to argue that, for whatever reason.
You did see philosophers claiming things like that back in the bad old days before Kant, which raises the question of what's changed. I suspect the reason is fairly mundane, though: before Kant (roughly), it was not only dangerous to be an atheist, it was dangerous to question that the existence of God could be proven through reason (because it would get you suspected of being an atheist). It was even dangerous to advocated philosophical views that might possibly undermine the standard arguments for the existence of God. That guaranteed that philosophers could used whatever half-baked premises they wanted in constructing arguments for the existence of God, and have little fear of being contradicted.
Besides, even if you think an all-knowing would also necessarily be perfectly good, it still seems perfectly possible to have an otherwise all-knowing being with a horrible blind spot regarding morality.
On the other hand, in the comments of a post on the orthogonality thesis, Stuart Armstrong mentions that:
This is not super-enlightening, partly because Stuart is talking about people whose views he admits he doesn't understand... but on the other hand, maybe Stuart agrees that there is some kind of conflict there, since he seems to imply that he himself rejects moral realism.
I realize I'm struggling a bit to guess what people could be thinking here, but I suspect some people are thinking it, so... anyone?