Why was the theory advocated by Brian Peterson, that the priests at Anathoth wrote down and edited the Deuteronomy flavored history from Joshua-2 King, worth considering? After all, you might say any adherent of Mosaic Yahwism could have taken up those themes.
One of the things that comes from carefully considering the data of the Hebrew Bible is just how much of a minority the advocates of the main biblical tradition were.
Most Israelite religion seems to have mixed the Moses tradition of one God with a cult involving the goddess Asherah, who many called the “Queen of Heaven”. People probably thought of her as the consort or wife of Yahweh/Baal, the King of Heaven. In the early days Baal was just another name for El or God. But after Jezebel and the incursion of a foreign Baal priesthood, there were violent attacks on both sides attempting to suppress the other’s form of worship.
So the question is where we are to look for communities that might have preserved the Moses tradition over several centuries. We can’t look to the royal palaces in the north or south. Most kings accommodated the mixed religion, even though there were occasional gestures at reform.
Priests were royal appointees, although there was a tradition to keep the priesthood limited within certain blood lines. This was an attempt to restrict the power of kings over religion. But it was a far cry from separation of church and state.
So even among the Levite and Zadokite priests there was only a minority that opposed the mixing of religions. Possibly, the Zadokites at the temple in Jerusalem adopted a theology that enabled them to withdraw from public life as a coping mechanism (Israel Knohl’s Sanctuary of Silence).
Among the prophets, the majority were probably what we would call false prophets, although one source of counter-religious tradition was the communities formed around certain prophets called the sons of the prophets.
Another possibility was the “people of the land” (probably the patriarchy of village elders) who installed some of the reform-minded Davidic kings in the south and probably existed in the north too.
Much of the Covenant Code in Exodus 21-23 and several complexes of law in Deuteronomy look like they originated as case law. Exodus 21:18-19 about what happens if two men (of different clans) get into a fight and one of them is hurt, but not fatally is a good example. The goal of the village elders would be to prevent an ongoing feud and limit destructive revenge. It was case law, but it was based on the idea that Moses instituted this kind of system (Exodus 18).
The village elders were probably also dealing with the draw of Canaanite fertility rites on rural people who depended on agriculture. However, the land-grabbing injustice practiced by the kings and their men (Ahab’s treatment of Naboth and the practices condemned by Micah) may have driven them to establish a system of Mosaic law over against royal law.
So the whole subject is very complicated.
What one has to look for is an old family that might have maintained both a counter-religious orthodoxy and an engagement with public life. Silent priests and scribes may have played a role, like monks in medieval times. Separatists, like the Rechabites (Jeremiah 35), might have played a role. Prophetic communities and priestly communities (the sons of the prophets, the sons of Korah, and the Asaph psalmists) may have played a role.
But if you are looking for continuity all the way to the 10th century or so, then a family with old roots near Jerusalem with a counter-religious attitude and ties to both the village elders and the Levites fits the bill. We know this was Jeremiah’s background. So, given the common traits between Jeremiah and the Deuteronomistic history, that one family in that one place stands out.