"Oedipus is punished not for any fault in himself, but for his ignorance. Not knowing his family history, unable to recognize his parents on sight, he is blameless; and in slaying his father and marrying his mother, he behaves as any sensible person might behave in the same circumstances." Do you agree with this interpretation?

This question is fairly subjective and could be answered in several different ways. It's true that Oedipus was ignorant of his actions before the play began and did not realize that the man he killed was his father or that the woman he married was his mother; therefore, one might feel that he is punished far too harshly. If you finished the play with the feeling that Oedipus's fate was unfair, then you likely do agree with the interpretation quoted above and should answer the question with textual evidence supporting this conclusion.
On the other hand, one could argue that Oedipus is punished not for his unwitting fulfillment of the prophecy of his birth (killing his father and marrying his mother), but rather for his fatal flaw of hubris, which guides his actions over the course of the play itself. Oedipus refuses to listen to the seer Tiresias or examine/change his behavior, because he is desperate to cling to his power. Because of this fatal flaw, one might disagree with the interpretation of Oedipus as "blameless." It is not the fact that Oedipus, in his ignorance, behaved badly that leads to his downfall; rather, he is punished because, when confronted with the truth of his actions, he refuses to listen or take responsibility. This is a subtle distinction but an important one.

Although the interpretation of Oedipus simply acting as any other person would under the same circumstances and being condemned because of it seems harsh, it does correlate with the text of the play. Among other things, Sophocles's Oedipus Rex is a treatise on the theme that fate is inescapable and ultimately powerful. Thus, it ascribes to a philosophically deterministic view.
It is completely true that Oedipus, his family, and all of Thebes (through the plague on the city) are punished because of Oedipus's ignorance of his own identity. All of the tragic events are known about and prophesied by the Oracle of Delphi and then Tiresias, but no alternative is given for their coming to pass. Indeed, Oedipus's true parents, Laius and Jocasta, as well as Oedipus himself, try to stop the prophecies from coming to pass, but they merely help to fulfill them through their efforts.