There is a sense in which both Oedipus and Jocasta, to a greater extent, willingly blind themselves by refusing to acknowledge the truth of various prophecies and omens regarding the true identity of the killer of Laius, the former King of Thebes. This is of course something that Jocasta in particular is rebuked for by the Chorus as they are very concerned about her attitude towards prophecy and omens and the gods in general.
Because Oedipus is so convinced that he can overcome his fate, he is blind to the fact that the events that transpire to put him on the throne are a part of that fate. I'm not sure this is quite moral blindness, though, as others have said, he was fated to kill his father and marry his mother. This is one of the fundamental tensions in the play- fate vs. human agency.
To the Greeks, the greatest moral blindness would have to be Oedipus's hubris in his thinking that he would outwit the Oracle and defy his fate as decreed by that Oracle. His is the most supreme arrogance to think that a mortal knows better than a god! When he tries to run away from his (adoptive) parents so as to avoid killing his father and marrying his mother, he actually ensures that he does actually do that to his REAL parents, Laius and Jocasta.
There is a simple connection in the minds of the Greeks. Pride or hubris leads to pride. The moral blindness that Oedipus possess is that he is proud. On account of this, he is filled with ignorance. He does not who he is and what he has done. These are the furthest things from his mind. In addition, he drives the play through his pride. He thinks he can solve any problem. It is only when he is confronted powerfully that he finally is able to see.
I think we see moral blindness in Oedipus Rex when Oedipus does not want to hear what Teiresias, the prophet, has to say. In fact, rather than paying attention to the fact that Teiresias really doesn't want to tell Oedipus what he knows at all, he insists that it is a plot commandeered by Creon, who Oedipus sees as a threat to his throne. He is blind to what is really important: finding who killed Laius. Instead, he assumes an "all about me" attitude, when ironically, it IS all about him.
The person who seems most obviously "morally blind" in this play is Oedipus, whose determination to find the truth and then act on it leads, ironically, to his own tragic fate. It is one of the great paradoxes of the play that Oedipus, in trying to do the "right" or moral thing, brings so much suffering down upon himself and especially upon Jocasta.
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.