In The Name of The Father, & The Son, & The Holy Ghost. Amen.
A rather widespread misconception prevalent in Catholic circles today, thanks to Nostra aetate, is that Jews are Israelites, both spiritually and physically!
This notion must be rejected by Catholics on both accounts. The Catholic Church has taught since its very inception that Jews are no longer spiritually Israel as will be shown later in this post.
As for being physically Israelites then this notion must be rejected as well. Rabbinic Oral Law teaches that Gentiles can becomes Israelites by conversion. This has happened on a very large scale in Jєωιѕн history and most Jews can no longer be called Israelites to indicate that they are of pure Hebrew ancestry. It is safe to conclude based on what we know today of genetic studies that the notion of a pure Hebrew people died a long time ago. The Jews have mixed with the nations they have been dispersed in. That is why Ethiopian Jews look like Ethiopians, αѕнкenαzι Jews look EurAsian, Sephardi/Mizrahi Jews look middle eastern, Chinese Jews look Chinese, etc.
As for Catholic Church teaching on spiritual Israel then please read the following:
1. Justin Martyr (AD 100–165), who defended Christianity against a Jєωιѕн enemy, claimed Christians “are the true Israelitic race,” and asserted that the Biblical expression “the seed of Jacob,” when properly understood, now refers to the Christians, not the Jews. Alexander Roberts and James Donaldson, eds., Ante-Nicene Fathers, vol. 1 (Peabody, MA: Hendrickson Publishers, Inc., 1994)
2. Tertullian (AD 145–220), prominent church theologian from North Africa, interpreted God’s statements to Rebekah concerning the twins (Esau and Jacob) in her womb (Genesis 25:23) in the following manner: Esau, the older brother, represents the Jews; and Jacob, the younger brother, represents the Christians. He indicated that God thereby revealed that the Christians would overcome the Jews and that the Jews would serve the Christians. Alexander Roberts and James Donaldson, eds., Ante-Nicene Fathers, vol. 1 (Peabody, MA: Hendrickson Publishers, Inc., 1994)
3. Cyprian (AD 195–258), bishop of Carthage, stated that he “endeavoured to show that the Jews, according to what had before been foretold, had departed from God, and had lost God’s favour, which had been given them in past time, and had been promised them for the future; while the Christians had succeeded to their place, deserving well of the Lord by faith.” Alexander Roberts and James Donaldson, eds., Ante-Nicene Fathers, vol. 1 (Peabody, MA: Hendrickson Publishers, Inc., 1994)
4.And first of all, by the death of our Redeemer, the New Testament took the place of the Old Law which had been abolished; then the Law of Christ together with its mysteries, enactments, institutions, and sacred rites was ratified for the whole world in the blood of Jesus Christ. For, while our Divine Savior was preaching in a restricted area — He was not sent but to the sheep that were lost of the house of Israel — the Law and the Gospel were together in force; but on the gibbet of his death Jesus made void the Law with its decrees, fastened the handwriting of the Old Testament to the Cross, establishing the New Testament in His bƖσσdshɛd for the whole human race. “To such an extent, then,” says St. Leo the Great, speaking of the Cross of our Lord, “was there effected a transfer from the Law to the Gospel, from the ѕуηαgσgυє to the Church, from many sacrifices to one Victim, that, as our Lord expired, that mystical veil which shut off the innermost part of the temple and its sacred secret was rent violently from top to bottom.”
On the Cross then the Old Law died, soon to be buried and to be a bearer of death, in order to give way to the New Testament of which Christ had chosen the Apostles as qualified ministers….
But if our Savior, by His death, became, in the full and complete sense of the word, the Head of the Church, it was likewise through His blood that the Church was enriched with the fullest communication of the Holy Spirit, through which, from the time when the Son of man was lifted up and glorified on the Cross by His sufferings, she is divinely illumined. For then, as Augustine notes, with the rending of the veil of the temple it happened that the dew of the Paraclete’s gifts, which heretofore had descended only on the fleece, that is on the people of Israel, fell copiously and abundantly (while the fleece remained dry and deserted) on the whole earth, that is on the Catholic Church, which is confined by no boundaries of race or territory.
(Pope Pius XII, Encyclical Mystici Corporis, nn. 29-31)
5. On the interpretation of Rom. 11: 25-32
From the present, [vv.] 1-24, St. Paul turns his attention to the future. The time will come when the present problem of Israel’s exclusion from the salvation of the Messias will cease to exist because of her conversion, which will follow upon the conversion of the Gentiles.
(Dom Bernard Orchard et al., A Catholic Commentary on Holy Scripture [London: Thomas Nelson & Sons, 1953], n. 859i, p. 1072].