Maybe one of his parents was Eastern Orthodox, and his belief in Christ led him to embrace that particular expression of the Christian faith.
By the way,Chrysostom was pretty critical of Christians. One of his most famous quotes is "The road to hell is paved with the skulls of priests". I've never read his anti-Jewish rhetoric in context; I've read one quote of his about the Jews, and it looked horrific.
Yes, I am sure that is probably it.