No, they are some of the descendants of the original Jews. They became merchants because those were the ones who survived the great genocide of the Roman-Jewish wars which probably exterminated 50-70% (or more!) of the world's Jewish population. Those in Isreal were dead. Mainly Christian Jews (because they would submit to Rome) and Jews abroad survived.
I see way too many bad theories out there about the Jews, people don't know their history because they neglect the Jewish Roman Wars. Everything starts there and they were some of the most influential and important wars in all of history. For God's sake, Isreal did not recieve a substantial population of Jews again for nearly 2000 years the genocide was so great, total, and complete in it's nature. The earth was even salted in many places afterwards I believe.
If men want to understand what is happening now, men must understand what was happening then. The split between the Jews who accepted Christ in the wake of the destruction of Jerusalem is what created Christianity:
"They first called themselves Christians at Antioch." - Acts 11
The Jews who still refused to convert became Talmudic, their rabbinical oral tradition. There is no other history that explains things as well as this, the idea that some other group came in and became Jews makes no sense, why would anyone care about Judaism unless they believed their ancestry to link to David and Moses?
I don't disagree with any of your statements. I've made the case in the past when arguing with MusicForThePiano that they may very well be carrying the authentic lineage of the Israelites, but that that doesn't carry any weight in so far as they oppose Christ. If you religiously oppose Christ and all he signifies, then you are a part of the Synagogue of Satan, no matter who you descend from.
Here's the thing though, lineages have never been sanctifying in themselves, even before Christ. The reason lineages were kept among the ancient Israelites was because they had a prophetic context. They were meant to verify the ancestry of the messiah and his prophet. Just like the so-called old covenant law. It had revelatory significance, not soteriological significance, as St Paul explained in detail.
What Jews believe about their ancestry is irrelevant, as they don't keep the lineages any more so there's nothing to be learned from them. They can't tell from what tribe any of them descends, rendering messianic prophecies useless.
Given that matrilinearity is a medieval invention, there are probably more Christians carrying actual Israelite lineages than Rabbinic Jews. And if they didn't, that wouldn't matter either.
If a goy converts to Judaism for whatever reason as has happened numerous times in the past, who am I to say that he's not a real Jew? He religiously opposes Christ and fancies himself a descendant of Judah. That wouldn't sanctify him either way, it's only relevant regarding messianic prophecies, which have no meaning if you oppose the actual Messiah.
My interest in how the change towards urban mercantilism happened is not religious in nature. It's just curiosity. Jews had been doing mass conversions at several points in time, and they didn't have a strong genetic perspective on it until much later. Jews weren't a race, they were a people based on faith. You didn't become an Israelite by birth, but by circumcision, it just coincided with ethnicity because all religions did at that time. I'm not sure whether and to what degree those people could be included in the ancient lineages, but since those don't exist any more, that's neither here nor there anyway.