That is true, although I suspect the Jewish exiles would be immersed in Persian culture while only transferring a smidgen or two of Jewish culture in the other direction.
Why would they be immersed in Persian culture? They were exiled to Iraq by the Babylonians, not Iran. The Persians sent them back home. Now obviously a lot did not go and we do find Jews living in Iran as in the story of Esther and Mordecai, but it would be an exaggeration to say that Jews as a whole were immersed in Persian culture.
I think most of the Jewish influence would be in cooking, art, music, crafts, etc. Religious jobs would probably be closed to Jews, so their influence would be small. Meanwhile the Jews would be under great pressure to adopt the culture and religion of the Persians.
As I indicated earlier most of the influence that can be documented occurs during the Hellenistic period when both Jews and Zoroastrians are being oppressed by the Greeks.
Also, if we agree that the Jews were originally polytheistic and at most monolatrous, then dualism was inherent.There was the good god Yahweh and the bad gods of the foreigners.
I disagree. The Tanakh does not indicate that other gods are bad. Jews were told to worship Yahweh because He is the one who brought them out of Egypt and they owe it to Him.
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