I assert that people say something is right/wrong only basing on their desires. They do not want X to be done, either under particular circumstances or any. Desires, indeed, are real. Therefore, moral statements are relating to desires and, as follows from previous sentence, reality.
At the same time, desires are subjective: different people can have different and mutually contradictive desires. Therefore, such theory of morals would imply there are many systems of morality and neither of them is false, because they are based on desires, which are real.
My position is completely cognitivist: people are making moral judgements not necessarily in order to make others not to do things they think are wrong. They can do it in order to describe their mental state. The sentence "I'm hurt" has cognitive meaning, so can moral statements.
Further explanation regarding my position:
People act only in accordance to desires and reflexes. Desires relate to conscious part and reflexes - to unconscious.
Desires can contradict each other. Then the strongest desire takes over.
Everything that people do consciously, they do only in accordance with their will. If you see your friend passing by, you are greeting them. If not - you don't. Now, using analogy: if you see an extortioner threating you and you can't defend yourself, you give money. If not - you don't. Indeed, you would not want for such a situation to happen, but when it happens, other desires come into effect, relating to the reality and the possibility. Out of all possible actions people act in accordance with the most desirable. Some impossible actions may be even more desirable, but they are impossible and people must follow other desires then.
Also, reflexive utterances regarding rightness and wrongness do not belong to cognitive utterances and, therefore, are not a part of this discourse.
So, is it possible to be both moral realist and ethical subjectivist?