There are no pureblooded Jews that exist in the world (barring the possibility of supernatural activity such as immaculate conceptions). Purebloodedness isn't even a Biblical concept. Being a descendant of someone does not mean that you must be a pureblooded descendant. Who fed you this story about purebloodedness?
Revelation 7 talks about 144,000 from the tribes of the children of Israel. 12,000 of those are from the tribe of Judah (Jews). Another passage describes the 144,000 being virgin men that never knew the touch of women. In your view can someone be both a descendant of Judah at the same time as being a descendant of Benjamin?
Also, when Paul mentions that he is from the tribe of Benjamin, does he suddenly no longer count as being from the tribe of Benjamin because he turned to Christ? No. So why then would any of the 144,000 be required to identify as NonChristian Jews in order to qualify to be counted in that number?
No. One can by definition be of Jewish descent at the same time as being of nonJewish descent. They aren't mutually exclusive statuses. Timothy is an example of someone in the NT that very explicitly fits into the category of being both from Jewish and nonJewish ancestry.
We see OT permissibility of proselytes being welcomed into the tribal houses (e.g. Egyptians after the third generation in Deuteronomy). The idea of any Jewish person being "pureblood" makes absolutely no sense and is contrary to established Biblical practices. And we see empirically that Jews and Arabs descend from Canaan. More than that, even Abraham was born from nonJew parents, meaning that every Jew also descends from nonJews/nonIsraelites/nonHebrews.
If humans were asexually reproducing organisms, I might agree with your interpretation. But we aren't asexually reproducing organisms and therefore your premise doesn't make sense.