Simply because someone calls himself a Jew does not prove that he is a true physical descendant of Jacob/Israel. Just as people from many different races and nationalities are referred to as Americans merely by virtue of their being a United States citizen, so the Romans also referred to all the inhabitants of Judea as Judeans (Jews in modern parlance), regardless of whether they were Israelites by blood or not.
"John Hyrcanus conquered the whole of Edom and undertook the forced conversion of its inhabitants to Judaism (Joseph., Ant. XIII, 9, 1). Thenceforth the Edomites became a section of the Jewish people." (Encyclopedia Judaica, Vol. 6, (1971), p. 378; The New Standard Jewish Encyclopedia (1977), p. 589).
"Thus, at this juncture of time the Edomites 'were incorporated with the Jewish nation, and their country was called by the Greeks and Romans 'Idumea' (Mark 3:8; Ptolemy, 'Geography,' v. 16)." (The Jewish Encyclopedia, Vol. V. (1904), p. 41).
Flavius Josephus Antiquities of the Jews Book XIII
CONTAINING THE INTERVAL OF EIGHTY-TWO YEARS,
FROM THE DEATH OF JUDAS MACCABEUS TO THE DEATH OF QUEEN ALEXANDRA.
CHAPTER 9.
HOW, AFTER THE DEATH OF ANTIOCHUS, HYRCANUS MADE AN EXPEDITION AGAINST SYRIA, AND MADE A LEAGUE WITH THE ROMANS. CONCERNING THE DEATH OF KING DEMETRIUS AND ALEXANDER.
1. BUT when Hyrcanus heard of the death of Antiochus, he presently made an expedition against the cities of Syria, hoping to find them destitute of fighting men, and of such as were able to defend them. However, it was not till the sixth month that he took Medaba, and that not without the greatest distress of his army. After this he took Samega, and the neighboring places; and besides these, Shechem and Gerizzim, and the nation of the Cutheans, who dwelt at the temple which resembled that temple which was at Jerusalem, and which Alexander permitted Sanballat, the general of his army, to build for the sake of Manasseh, who was son-in-law to Jaddua the high priest, as we have formerly related; which temple was now deserted two hundred years after it was built. Hyrcanus took also Dora and Marissa, cities of Idumea, and subdued all the Idumeans [Edomites, descendants of Esau]; and permitted them to stay in that country, if they would circumcise their genitals, and make use of the laws of the Jews; and they were so desirous of living in the country of their forefathers, that they submitted to the use of circumcision, and of the rest of the Jewish ways of living; at which time therefore this befell them, that they were hereafter no other than Jews.
KJV Romans 9:13 As it is written, Jacob have I loved, but Esau have I hated.
The Wars of the Jews
Or
The History of the Destruction of Jerusalem Book II
CONTAINING THE INTERVAL OF SIXTY-NINE YEARS.
FROM THE DEATH OF HEROD TILL VESPASIAN WAS SENT TO SUBDUE THE JEWS BY NERO.
CHAPTER 8.
ARCHELAUS'S ETHNARCHY IS REDUCED INTO A [ROMAN] PROVINCE. THE SEDITION OF JUDAS OF GALILEE. THE THREE SECTS.
2. For there are three philosophical sects among the Jews. The followers of the first of which are the Pharisees; of the second, the Sadducees; and the third sect, which pretends to a severer discipline, are called Essenes. These last are Jews by birth, and seem to have a greater affection for one another than the other sects have. These Essenes reject pleasures as an evil, but esteem continence, and the conquest over our passions, to be virtue. They neglect wedlock, but choose out other persons children, while they are pliable, and fit for learning, and esteem them to be of their kindred, and form them according to their own manners. They do not absolutely deny the fitness of marriage, and the succession of mankind thereby continued; but they guard against the lascivious behavior of women, and are persuaded that none of them preserve their fidelity to one man.
KJV Romans 2:29 But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.
Yahweh will not save anyone who rejects his Son Yahshua as Savior and Lord, regardless of whether they are descended from Yacob/Israel or not. Yahweh owes nothing to any man or nation on this earth. We serve, love, and glorify Yahweh and His Son Yahshua, or we die.
KJV Romans 9:27 Esaias also crieth concerning Israel, Though the number of the children of Israel be as the sand of the sea, a remnant shall be saved: