According to the Bible, they* were* that tribe - as in, the whole lot of them went to Egypt.
No, incorrect - Moses married into aMidianite clan - while supposedly descended from Abraham like the Israelites, they were not monotheistic. They may have been henotheistic (like the pre-Exile Hebrews probably also were, historically), but certainly weren’t monotheists.
The sons of Jacob (and presumably their extended families) go to Egypt, but presumably the other decendents of Abraham stay. I think that’s the OP’s question, what happened to them? I’d say the bible suggests the decedents of Midian, at least, stayed put and continued the tradition outside of Egypt.
According to wikipedia, Jethro worshipped the God of Abraham, which is what I meant by monotheistic. Your right henotheistic is probably more accurate, but in anycase, both he and Moses were of the same religion, which is what I was getting at.
AFAIK, only the Israelites worshipped a “single Almighty God”, which is what the OP was asking. Other descendants of Abraham (like the Midianites, also the Moabites and Edomites) were *not *monotheists. They seemed to all partake of the pan-Levantine El-Asherah-Ba’al pantheon (As, probably, did the pre-Babylon-Exile Jews.)
I think, and I could be wrong, that Jethro only becomes a worshipper of what we would understand as “God” after Moses becomes his prophet - i.e. post-Burning Bush. Before that, the god he worships (El Shaddai) is not really what we would understand as the Israelite god.
Are you asking in terms of what is taught in the Bible or in terms of archaeological history?
Archaeologically speaking the Exodus probably didn’t happen (or at least was no more than a vast exaggeration of a much smaller event that happened to a small group of people) and the Jewish people didn’t start believing in a single god pretty much right up to the point where the Tanakh was completed.