Since I include Christians under the heading of 'Jew', I have no interest in the stupidity of merely having the right genealogy making one 'Jewish' when it comes to theology. Ethnic Judaism being 'The Chosen' is a racial supremacy myth invented by the post-exilic Babylonians on their return to the homeland, wherein they used Cyrus's support to oppress Ethnic Jews who remained behind, making them second and third class citizens for the most part, and create a superiority of bloodlines for themselves, via fake genealogical and the like and appointing themselves rulers of the state. They pretty much killed off the covenants as a basis for advancing the culture and society, and it stagnated as is always the case when racist nonsense becomes the basis for rulership and law. Merely being sa 'pure Jew' is just tribalism, and has nothing to do with the covenants; those are a two way street, and only Jews who actively pursue their end of the deals are 'The Chosen'. This racism finally killed off the temple-state, and the racist frauds lost a lot of power to the Christian sects, which had much more appeal as opposed to supporting a priesthood that only used most Jews as a cash cow and as inferiors, particularly the Hellenistic Jews and even some Pharisees; Christianity was interested in actually fulfilling the covenants, i.e. to make their theology 'a light unto the world', a universal message of hope and a radical reshaping of society. The fake Jews focused on murdering as many Christian as possible, and trying to convince others that they were inferior races who should be worshiping pure Jews' as some Master Race. They ended up with their Temple destroyed and scattered yet again, while the Evul Xians went on to revolutionize the West.
Up to the present, it has not been sufficiently recognized that from a social point of view the whole community of Judaism at the time of Jesus was dominated by the fundamental idea of the maintenance of racial purity. Not only did the priests, as the consecrated leaders of the people, watch anxiously over the legitimacy of priestly families, and weed out all priestly descendants born of an illegitimate union; but the entire population itself, in the theory and practice of religious legislation at the time of Jesus, was classified as to purity of descent. Only Israelite of legitimate ancestry formed the pure Israel. All families in which some racial impurity could be established were excluded from the pure seed of the community. As in the case of the priesthood, the reason for this was a religious one; the nation was considered God-given and its purity was God's will; the promises of the age were valid for the pure seed.
Prologue to Part IV, The Maintenance of Racial Purity of Joachim Jeremiah's Jerusalem in the Time of Jesus{/b]. Following sections include chapters on topics such as the historical value of lay genealogies, which includes an enlightening discussion on the alleged 'discrepancies' between Matthew's and Luke's genealogies of Jesus' line of ancestry, and a discussion of forged genealogies for a later Jewish priest , R. Judah I, giving him a Davidic origin, even though in his own auto biography he admits to being in the Benjaminite line of ancestry. Also chapters on the Samaritans, Gentiles, ,despised trades', civil rights of 'full Israelites', detailed laws regarding 'illeglimate Israelites', and so on.
No wonder Christians were so popular with a lot of Jews; the legalisms reached absurd levels and pretty much alienated most citizens by the time Jesus and other sects came along. The Qumran sects isolated themselves over considering the priests not of the line of Zadok to be 'illegitimate' an Herod's appointees to be 'illegal' as temple heads.