I’m no expert here. It seems to this novice that all belief forms potentially influence each other, especially if they in close contact. Thus, Egyptian mono- and polytheism, Canaanite religions, Sumerian religion, Babylonian and Persian religions, and then Greek, Roman, Christian and Islamic thoughts likely all influenced Jews as they lived near or among them (and vice versa). As a member of a tiny minority Christian group in Niger, West Africa, growing up, we were strongly influenced by Islam in what we thought about and how we dressed (so as not to offend our neighbors). I’m certain that my own psyche developed differently from my extended family’s Christianity, because I grew up in an Islamic area and they grew up in a largely Christian one.
When I was in undergrad, the prof questioned if the Hebrews picked up monotheism from Egypt. I wrote on my test, questioning whether the Egyptians could have picked it up from the Hebrews. I’m not sure.
In cultural anthropology, we learned that populations who are in a strong city or state with a central ruler tend to adopt monotheism more rapidly than those who are in small, scattered, hunter gatherer groups. In that case, it’s rather amazing that the herding Hebrews maintained a relatively strong monotheistic tradition (even though they did struggle with syncretism from the surrounding religions). John Patrick alluded to Deuteronomy 11: 18-21 shows the strength of tradition in passing on monotheistic belief (consider also the Shemah):
18 Therefore shall ye lay up these my words in your heart and in your soul, and bind them for a sign upon your hand, that they may be as frontlets between your eyes.
19 And ye shall teach them your children, speaking of them when thou sittest in thine house, and when thou walkest by the way, when thou liest down, and when thou risest up.
20 And thou shalt write them upon the door posts of thine house, and upon thy gates:
21 That your days may be multiplied, and the days of your children, in the land which the Lord sware unto your fathers to give them, as the days of heaven upon the earth.
The rise of Islam from a polytheistic tribe in Arabia also seems to break the rule, though Mohammad was thought to have received Christian influence.
I do think that if God is just, and cares for justice as much among the Persians as among the Jews, He’s going to work on all of them to bring them closer to himself, regardless of their state of knowledge.