Several issues:
1. most if not all non-Judah tribes of Israel (save Benjamin at Galilee) were most likely in exile or scattered or the like at the time Jesus arrived.
2. the idea of any organic Judahite being in exile at the time with John in the wilderness may have been because the Edomites didnt' want anything to do with the original doctrines;
3. the notion of Y'shua/Jesus being the son of an Edomite-Judahite is highly questionable;
4. the notion of Y'shua/Jesus being clearly non-Edomite makes more sense as to why the Edomite-Judahite factions may have been against him.
5. I recall analysis pointing to Y'shua/Jesus having been hanging out with the Benjaminites and the Essenes in northern Judea.
6. there are those who assert that those called for the death and crucifixion of Y'shua clearly identified themselves with Essau/Edom by admitting that they had never been in captivity which might be true of Edom/Essau's or the Edom-Cain lines rather than being true of Israel/Jacob;
7. its important to avoid blurring the distinctions between
Jesus son of Julius Pantera and the Y'shua the Anointed;
8. The saints aren't referred to as being gentiles in the Bible but as "formerly gentiles".