Well that pretty much is the point, isn't it? Up until the time of Christ and the apostles, the Jews were very careful about the maintenance of records, measuring one's Jewishness through the father, as we see in places like Genesis 5 or Matthew 1. Temple records were kept and it was pretty easy to verify claims. Jesus’ lineage could be traced to Adam, nevermind Abraham.
But since the destruction of the temple in AD70 the possibility of following the old covenant norms for judging lineage have passed away. In its place is the invention of the rabbis.
But you want to answer the question of what "Israel" means when it is used in the Bible with respect to the future by appealing to the modern rabbis. This strikes me as an unsatisfactory position for what seems to me to be rather obvious reasons.
Lineage was only important until Christ appeared. That is because it was only necessary to estanlish His lienage wrt David and Abraham. Jesus is the true Israel, the fulfillment of all the old covenant types. So the matter of lineage today really doesn’t matter. All one needs to do is to be found "in Christ" and the blessing of the promises accrue to him. You just need to establish your spiritual relationship. That is all that matters. Today, the true children of Abraham are those who by faith have come to Christ.
I have a friend named Avi who claims to be Jewish. His rabbi makes the same claim. What passage in the bible tells me whether Avi is or is not Jewish?
"But since the destruction of the temple in AD70 the possibility of following the old covenant norms for judging lineage have passed away. In its place is the invention of the rabbis."
At the risk of appearing to be obnoxious, I think that your post is extremely worthy of insult, but I'll hold off. It is a holiday after all.