For this question, I would like to take the axiom of moral realism, as defined by SEP:
moral claims do purport to report facts and are true if they get the facts right. Moreover, they hold, at least some moral claims actually are true.
If I am correct, it seems that one could be a moral realist and believe that morality has no normative force, so the moral ought must be justified further, it is not entailed from moral realism.
I can think of two formulations of the normativity of morality:
1. Moral oughts, i.e. you ought to do/be x because x is morally good.
2. Rational oughts from moral facts, In as far as you ought to be rational based on non-moral facts, you ought to be rational based on moral facts, just as you act in a certain way because the sky is blue, you should act a certain way because x is wrong.
I do not accept formulation 1, for reasons articulated by many philosophers, one among them Schopenhauer:
That ought has any sense [Sinn] and meaning [Bedeutung] at all only in relation to threatened punishment or promised reward. Thus, long before Kant was thought of, Locke already says: ‘For since it would be utterly in vain, to suppose a rule set to the free actions of man, without annexing to it some enforcement of good and evil to determine his will; we must, where-ever we suppose a law, suppose also some reward or punishment annexed to that law.’ (On Understanding, Bk. II, ch. 33, §6). So the ought is necessarily conditioned by punishment or reward [...]. But once those conditions are thought away the concept of ought remains empty of sense. (BM §4, 123)
And further arguments from this paper
I also don't accept formulation 2. Firstly, it is not clear to me that one ought to be rational 1. But even if I take the axiom that one ought to be rational, would that entail obeying the moral principles?
Rationality: the purely internal matter of having one’s mind in good order, regardless of how this matches up to external facts. As Kolodny describes it, rationality is “about the relation between your attitudes, viewed in abstraction from the reasons for them.”1
It's not clear to me that it is more rational to obey moral principles than it is not to. One can just as easily have a coherent set of beliefs that result in action that does not act in accordance with the moral truths. For example, using non-moral facts, my coherent set of beliefs could entail that I act as if the sky is not blue, if this disposition was altogether better for me. It isn't clear to me why this would be irrational.
So my questions are, have I missed any formulations for the normativity of moral beliefs, and what reasons do moral realists have for believing morality has normative force? Further, I wonder how common it is for a moral realist to not believe it entails normative force?