Tricky question, for three reasons:

1. Our primary source on the subject of Israelite culture and religion is the Bible, which, we can fairly say, has an agenda that doesn't lend itself to admitting to outside influences.

2. Scholars can't agree about what Israelite religion looked like before the Babylonian Exile. Old Testament/Hebrew Bible scholars divide into camps regarding how much of the Jewish Bible existed, and in what form, before the Jews returned from Babylon in the second temple period.

The answer to that question determines the baseline for comparison to post-exilic Judaism. E.g., was second temple Judaism an attempt to redefine pre-exilic Judaism of an attempt to return to it? Were the scribes trying to recover their traditions or justify their current practices?

3. Despite all of this, we do know there is a lot of influence by Ancient Near Eastern cultures on the Israelites, but it's hard to say how much of it came from interactions with empires before the Babylonian exile and how much came during the captivity. We find strong parallels to Assyrian and Babylonian imperial policies and theologies throughout the Hebrew Bible, from the language of covenants to poetry in the Psalms. There are a subset of scholars who see the Israelites as just a quirky offshoot of the politics, culture and religious practices of the region, but others simply see bits of the ancient near east leaking into an otherwise unique culture.