In science, a proposition about the world can generally be proven or disproven with arbitrary probability, so you can become as sure about it as you like if you invest enough resources.

In moral realism, propositions are purely logical constructs, and can be proven true or false just like a mathematica proposition. Their truth is one with the truth of the axioms used, and the axioms can't be proven or disproven with any degree of certainty; they are simply accepted or not accepted. The morality is internally consistent, but you can't derive it from the real world, and you can't derive any fact about the real world from the morality. That sounds just like theology to me. (The difference between this and ordinary math or logic, is that mathematical constructs aren't supposed to lead to should or ought statements about behavior.)

I will read Greene's thesis, but as far as I can tell it argues against moral realism (and does it well), so it won't help me understand why anyone would believe in it.