Cognitive dissonance requires one to hold two contradictory ideas or beliefs.
What idea or belief about this incident - about which we know almost nothing - could anyone have at this point that contradicts a previously held idea or belief?
Zimmerman has a history of aggressive behavior that gets him into trouble with the law, therefore he is likely to be the aggressor in this incident. Problem is, Apperson has a history of aggressive behavior that gets him into trouble with the law.
Zimmerman was the first to use deadly force in a prior incident, therefore he is an unstable maniac who normal people would reasonably fear. Problem is, Apperson was the first to use deadly force in this incident, and the police believe it was unprovoked.
Zimmerman got away with murder by cleverly exploiting loopholes in Florida's unjust doctrine of self-defense. Problem is, Apperson might try to get away with attempted murder by cleverly exploiting loopholes in Florida's unjust doctrine of self-defense.
Zimmerman likely was morally guilty of murder (if not legally guilty) because he was charged and prosecuted with murder. Problem is, Apperson has been charged and will likely be prosecuted with attempted murder, so he is likely morally guilty, even if he is acquitted.
Zimmerman might be a racist because he is a White Hispanic who "stalked" a black person who was doing nothing wrong. Problem is, Apperson might be a racist because he is a white person who "stalked" a Hispanic person who was doing nothing wrong.
So there would be a lot of cognitive dissonance involved in continuing to believe that Zimmerman was in the wrong, and Apperson was justified, given the developments so far. And for the record, we now know quite a bit about this case, not almost nothing.