Back to the original question:
The "New Covenant" was made in accordance with Hebrew scriptures, promises, and instrctions, never to be seperated or annulled by the "religion of men".
Jeremiah 31:31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah:
and
Hebrews 8:8 For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah:
Jesus continued in the fulfilling this promise with statements such as His instructions to His disciples: , Matthew 10:5-6 These twelve Jesus sent forth, and commanded them, saying, Go not into the way of the Gentiles, and into any city of the Samaritans enter ye not: But go rather to the lost sheep of the house of Israel.
And, His statement concerning His own ministry in Matthew 15:24 when confronted by a Gentile woman seeking His help: "But he answered and said, I am not sent but unto the lost sheep of the house of Israel."
But, also as foretold in the Tanakh, the new covenant would be opened up to the entire world - so that those who would respond (those called by the Spirit) would be accepted as grafted into the family of Abraham (Romans 11:14-36) and
by adoption into the Spirit of God (Romans 8:15-16), into the Nation of Israel (Romans 9:3-16), as children of God (Galatians 4:3-7, Eph 1:3-14).
While the followers of The Way were initially all Hebrews, the "sect" of Judaism that was foreordained as promised to Abraham (all nations shall be blessed ....), with the demise of the second Temple and the supporting priesthood, the religion of the Jews was "transformed" (not replaced) into the ever expanding redemption of the Gentile world, as members of the "chosen people, a holy nation".
It was by the acts of the Emptor Constantine that formalized the division, the splitting apart, the Christian faith from its Hebrew roots and made it a "separate religion". This is where the change of the Sabbath was officially changed from the seventh day to the first day (recorded as a "victory over the Jews"*), where Hebrew calendar was replaced by the Roman calendar for observing the Passover, and the resurrection of Jesus which was fixed to a particular first day observance. The term "Christ killers" was first recorded at this time (forth century).
For more such history of the Christian faith up through the fourth century from the western (Roman) world view, see Constantine's authorized church history, The Ecclesiastical History of Eusebius Pamphilus.
Conclusion:
For the most part, western Christianity of today is no longer a sect of Judaism; it is not even an outgrowth or a spiritual maturing of Judaism. It has, in truth transitioned into a separate religious movement – which should not be. There was intended to be only one body of Christ, not the fragmented mess we see today, even between the Jew and Gentile. Even so, in our own spiritual arrogance, for salvation we require Jews to join "the church" as Constantine envisioned it, not as Christ (chief cornerstone) and His Apostles (foundation) established it.
Even so, as the day of the Gentiles comes to its ordained close, the veil that has covered the eyes of the Jews for so long is being quickly removed. Over the past 60 years Messianic synagogues have been springing up all over the world, even in Israel – even in Jerusalem – there numbers continue to increase! (Do a Google search.)
Recommendation:
Let us get at least attempt to reconnected to our religious heritage and spiritual roots, and drop the pagan rites and ordinances of Rome and return to the worship of God as practiced by the followers of the Way during the first three centuries. After all, in the sight of God all believers in Christ Jesus are Jews, and our shared root is in Abraham.
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Sorry for the length.