One of the things that stood out to me while mirror-reading the Elohist Source, is the prominent issue that the author was dealing with in regards to immigrants in the land. Whether war, famine or some other cause, we don't' get much indication as to the reasons why aliens had immigrated to the Northern Kingdom, but we can see how the Elohist lays out expectations for them in the narrative.
When mirror-reading the Abraham Cycle, it seems that the Israelites were dealing with the descendants of Abimelech, as well as the descendants of Hargar's son living as aliens in the land of Israel. The Elohist approaches the issue from two sides. First, exclusion from the biggest entitlement program at the time, Abraham's inheritance. Only the descendants of Isaac were entitled to the inheritance, which meant Abimelech's and Hagar's son's descendants were excluded.
However, this exclusion is tempered by a call to treat aliens fairly. The Elohist does this by recounting Abraham's time as an alien in Gerar and showing how he was treated fairly by Abimelech, eventually culminating in a treaty that required the Israelites to treat the descendants of Abimelech fairly.
While, mirror-reading the Moses Cycle, the situation is different. The Kenites are not the same type of aliens that were in the Abraham Cycle. They were considered more of a minority than aliens. However, the Elohist approaches the issue from two sides again.
First, the Elohist makes is clear that Elohim is the God of the Hebrews, not the God of the Kenites, as in, He did not originate with them. On the flip side, the Elohist pushes inclusion. The Kenites were free to worship Elohim if they wanted to. This is most clearly seen in the narrative when the elders of Israel, Aaron and Moses sit with Jethro (a Kenite) in the presence of Elohim.