Could Sophocles' Oedipus Rex be a secular play ?
This strikes me as a rather interesting question, but I would say that from the ancient Greek perspective none of their plays could be regarded as secular because they were performed in honor of some divinity, namely Dionysus.
Also, a glance through Sophocles' play shows a deep concern with the validity of oracles and truth contained in oracles, especially those issued by Apollo at Delphi. Because the play is concerned with such religious matters, it is difficult to see how the play could be secular.
That being said, I'm sure that some modern staging of the play could manage to repress much of the religious content of the play and secularize it. Oedipus' continued blindness to the mound of evidence that he killed Laius strikes me a similar to the denial of wrongdoing that we frequently find on the lips of modern politicians.