The natural first response to this question is that morality and justice are not blind, they are, in fact, blinding.
All puns aside, there was no course of action that Oedipus could have taken to avoid his morally reprehensible fate. He tried to do the right thing, in his way, and failed because he was fundamentally incapable of overcoming his fate.
If we consider this inability as an unavoidable, fated fact then it becomes very difficult to think of Oedipus' deeds (incest & patricide) as moral acts at all.
He acts only out of his nature, as an animal might.