This would lead me to believe that somehow the bloodline, due to the fact it is traced through the father and not the mother, could in fact be traceable and pure ‘in that sense’ even though Gentile DNA was involved through some of the mothers. Am I all wet?
However, the bloodline, even if traced through the men alone, from this century down to the time of Christ really doesn't matter. It can be done. But what was the purpose of Israel? They were a light to the Gentiles. To that end they proselytized. By the time of Christ there were man Jews from many nations that came to the Feast of Pentecost, all mentioned in Acts chapter one. About 13 different nations are mentioned, each with their own language. Thus the gift of languages.
The Ethiopian Eunuch is an example of one such "Jew" who came to the Feast of Pentecost, and now was returning on his way back to Ethiopia. He was a proselyte to the Jewish Religion. A heathen would not be reading the Book of Isaiah. This man was a Jew, and he was black--from Ethiopia. This black Jew trusted Christ.
Now look at the list given in Acts one, and see if you can visualize color:
Acts 2:8-11 And how hear we every man in our own tongue, wherein we were born? Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia, Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes, Cretes and Arabians, we do hear them speak in our tongues the wonderful works of God.
Were all of these people the typical "olive-colored Jew," that we know of today, that we have stereo-typed in our minds? No, obviously not.
The blood lines run far into Greece, as many of the Jews of that day were Greeks.
Acts 6:1 And in those days, when the number of the disciples was multiplied, there arose a murmuring of the Grecians against the Hebrews, because their widows were neglected in the daily ministration.
Remember that the Septuagint was translated from Hebrew to Greek as far back as 250 B.C. so that the Hellenist Jews who did not understand Hebrew as their mother tongue, would be better able to understand the Scripture (OT).
A Jew (same as an Israelite) was one who had converted to Judaism. Color was not a factor at the time of Christ. Only more recently has ethnic bias become more of a problem.