Here is a scripture that I know that you posted or referenced, and it does give the basics
Galatians 3:
[26] For ye are all the children of God by faith in Christ Jesus.There are precursors to this in the OT, but I have too much work to do to chase them out presently.
[27] For as many of you as have been baptized into Christ have put on Christ.
[28] There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
[29] And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
Ephesians 1:5 Having predestinated us unto the adoption of children by Jesus Christ to himself, according to the good pleasure of his will,
Romans 8:15 For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
Galatians 4:5 To redeem them that were under the law, that we might receive the adoption of sons.
God does have something to say to those who say they are Jews and are not.
Revelation 2:9 I know thy works, and tribulation, and poverty, (but thou art rich) and I know the blasphemy of them which say they are Jews, and are not, but are the synagogue of Satan.
Revelation 3:9 Behold, I will make them of the synagogue of Satan, which say they are Jews, and are not, but do lie; behold, I will make them to come and worship before thy feet, and to know that I have loved thee.
Replacement theology will cause all kinds of problems.