It really doesn't matter.
Traditionally a Jew is introduced into the community by circumcision and Bar Mitzvah (and someimes "mikvah" - Jewish baptism), for males.
Bat mitzvah and mikvah for women, regardless of bloodlines.
Then who are these Jews to whom Paul speaks, religious or physical?
Rom 11:25 For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.
Rom 11:26 And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
Who is the “all Israel”? Anyone who happened to convert to Judaism in the last 2000 years or happened to be born to a Jewish mother? This is the problem. It seems for this to fit the dipsie view, the “ Jewish race” must have to have continued on since the times of Paul. There seems to be no other option since dispies also believe “generation” refers to race:
Mat 24:34 Verily I say unto you, This generation shall not pass, till all these things be fulfilled.
Last, if God desires that there be a group of "pure" bloodline Jews in the "end times" then He is able.
Yes, if He desires. But what evidence is there that He desires this?
While I am not a full fledged "dispensationalist" I believe that there are just too many unfullfilled prohecies to Israel that need closure for the Word of God to be finalized.
Not if Old Covenant Israel was a type and shadow of the New Covenant Israel.
What did Jesus mean by this:
Joh 1:47 Jesus saw Nathanael coming to him, and saith of him, Behold an Israelite indeed, in whom is no guile!
Was Jesus recognizing his ethnicity, or something more? It sems Jesus is saying he was more than a physical Jew but also a spiritual Jew.
When did the "end times" begin?
IMO, Friday the 14th May 1948 (Erev Shabbat 5th Iyar 5708) is a definite possibility.
Why, what prophecy does this fulfill?
IMO, every synagogue has the testimony of "The Torah" which stands as a fulfillment of Jesus words.
Matthew 5
18 For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled.
It is either fulfilled or not fulfilled. If it is not fulfilled, then none of the Law has passed. If it has been fulfilled then the Law has passed and so has "heaven and earth".It stays or goes as a whole.