Let's assume for the sake of this POD that Israel and Judah get smart kings/tribal leaders that decide to bow down to Assyria and Babylon, and are still in Canaan as independent kingdoms by the time of the Achaemenids. The POD is that the Jews are never deported and remain in Canaan by Babylon and Assyria. What happens?
Note-The United Monarchy and its existence or non-existence is irrelevant to this WI. The intelligence of the men running Israel and Judah, OTOH, is a big relevance.
Probably the biggest change is that the whole Rabbinic thread within Judaism never develops and Judahite/Israelite religion remains temple based, so no synagogue worship. This all developed as a means for the Jewish people to retain their religious, ethnic, and cultural identity in the face of the deportation by the Babylonians. This would have huge butterflies.
--Synagogue worship encourages Jewish males to learn to read, so they can recite the Torah in synagogue. Temple worship did not really do that...basically people went to Temple to make sacrifices to the Lord, not to study the Torah. So you have a much less educated Jewish/Israelite population in the ATL. As a result of that, you most likely do not have the sort of scholarship which lead to the standardization and canonization of certain books which became the Hebrew Bible (this sort of thing does not really benefit a Temple/Priest lead religion as it does one lead by rabbis...indeed, it gives the Priests the leeway to "interpret" the scripture in ways which will benefit themselves). And, as Carlton Bach pointed out, the religion would likely remain henotheistic,
--The whole Messianic thread within Judaism may well be stillborn. This is not something that the Temple Priests will like to have going on, as it poses a threat to the existing power structure.
--The development of synagogue worship lead by rabbis has enabled the Jewish people to survive as a separate people, even though for thousands of years they had no homeland of their own and were severely persecuted. Without that, it is much more likely that when Israel and Judah finally are destroyed...as was inevitable at some point in time, for they were simply too weak to stave off conquest indefinitely...the Judahite/Israelite peoples will simply be absorbed by the dominant culture of the surrounding peoples and disappear from history (as indeed happened to the Ammonites, Moabites, Edomites, Philistines, and all the other ancient peoples of that region). That, of course, would change history so radically that probably nothing of the world we live in today would be recognizable in the ATL.