According to Josephus, Alexander paid some homage to the Jewish High Priest at the temple of Jerusalem. When asked why he, a great king, would show respect to a priest, Alexander replied that he was not paying respects to the priest, but to the god who appointed that priest.

He then announced he had met their god when praying at Dios in Macedonia. He said that, coincidentally, the god had looked just like the High Priest, and that he had encouraged Alexander to boldly conquer the Persians by crossing the sea. Alexander then made sacrifice at the temple in thanks.

So, basically, Alexander set himself up as a messenger and believer of God, while still remaining a pagan himself. That said, he respected all of Jerusalem's traditions and institutions while he was there, and only later successors would begin their repression of the Jewish faith.