I am personally a moral realist. I believe that moral statements are reflective of ontological However, I don't think that moral realism can be proven or disproven. This is the best alternative to moral realism I've heard so far:
Societies have preferences for actions that lead to that society being sustained. So, in a sort of societal evolution (or Hegelian dialectic if you prefer), we end up with societies that hold those values that sustain them, such as "no murder." Values that are no longer necessary are eventually discarded (such as "no adultery," no longer necessary to the survival of the state because of the decline of things such as divine right, and the advent of birth control, etc.).
However, there may be some generally-held values that do not lead to society being sustained, or that are negative to society being sustained.
Neither of these positions is more testable than the other, meaning that while intrasystemic arguments can be settled via science and possibly reason (arguments that share certain first principles), intersystemic arguments cannot be proven or disproven. And so the only way to settle intersystemic conflict is persuasion. I may modify my theory to something more like this. Really, it's more like modern physics. There is a class of things in which Newtonian physics holds. There is a class of things in which relativity holds. And there is a class of things so bizarre that we don't know any rules yet that apply to them, or at least they break rules that hold in other places where Newton's rules are broken (i.e., zero energy particles). Similarly, i would hold that there are a class of arguments in which reason is applicable and ought to be respected (this would be a proscriptive belief, rather than a descriptive belief). There is a class of arguments in which science is applicable and ought to be respected. But there is another class, of which Moral Realism is an example, in which neither standard of proof is applicable, and as such, Persuasion is a justifiable means of arriving at a conclusion.