Why be moral? In most cases, the fact of the matter makes quite a difference. Belief that you can fly can get you injured or killed, if you, in fact cannot fly, Being wrong about the facts entails misjudgments, which may be benign, or beneficial, but usually are neither, I would think.
I don't see why "moral facts", should be different. It may be the case that not believing some inconsequential falsehood could be life threatening. Say, a position on the colour of the creator of the universe's ear hair -- but then, the prudent fact would be where and when to commit to what, and not the inconsequential details of what is committed to.
So, what does it mean for killing babies to be moral? Does it mean that God has deemed it so? Does it mean that babies emit a poisonous gas, or don't actually exist by are disguised psychic parasites?
I also don't see this question as being different than asking if one would change their opinions about any state of affairs, despite powerful reason to believe the contrary. One can have extremely deep conviction, and attachment in blue ear hair, even after death, and eyeballing that the orange ear hair crowd was right all along. If you were them, would you change your opinion?
So, three points: Facts matter, and when they don't, then who cares what the case is?
Why should there be a difference between moral facts, and other facts? If there is no difference, then they either matter, or don't matter, as facts. Thirdly, opinions about any state of affairs can be deep seated, and are rarely not emotionally charged at all. I don't see why asking the question about "moral facts" is different than asking it about any fact.