Paul named the two groups.
He designated himself as a jew.
He designated himself as a christian.
Look at your answers to those facts.
You can not grasp the two exist.
What you are doing is trying to make a multifaceted concept/ truth into one dimension.
Lots of concepts in the word are multifaceted truths.
That may help
Paul never designated himself as a 'christian'.
As a Jew he received his Messiah and Savior whereby his sins were washed away and he also received the Promise of the Father = Holy Spirit
Now Paul becomes a 'True Jew' in the Spirit where God always intended the Jewish People to Dwell and Walk IN.
Gentiles who receive the Lion of the Tribe of Judah as their Savior are adopted into the Israel of God and become FULL and COMPLETE Members of the Household of God, lacking no good thing in Yeshua HaMoshiach their Savior.
Galatians ch3
Is the law then against the promises of God? Certainly not! For if there had been a law given which could have given life, truly righteousness would have been by the law.
22But the Scripture has confined all under sin, that the promise by faith in Jesus Christ might be given to those who believe.
23But before faith came, we were kept under guard by the law, kept for the faith which would afterward be revealed.
24Therefore the law was our tutor
to bring us to Christ, that we might be justified by faith.
25But after faith has come, we are no longer under a tutor.
26For you are all sons of God through faith in Christ Jesus.
27For as many of you as were baptized into Christ have put on Christ.
28There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.
29And if you
are Christ’s, then you are Abraham’s seed, and heirs according to the promise.
In our flesh their are "Jews and Gentiles" but not in the SPIRIT.
For if you are in Christ, then you are a "son of God".
Notice what the Apostle John says of this: 1 John 3:1-3
Behold what manner of love the Father has bestowed on us, that we should be called children of God! Therefore the world does not know us, because it did not know Him. Beloved, now we are sons of God; and it has not yet been revealed what we shall be, but we know that when He is revealed, we shall be like Him, for we shall see Him as He is.
And everyone who has this hope in Him purifies himself, just as He is pure.
QUESTION: What did the Apostle John omit from his Epistle and specifically from 1 John 3:1-3?