A Christian is a Christian. That is not an ethnicity like American.
You had just said that you can't add ethnicity to "American". Now you imply "American" is an ethnicity - (unless you meant "Just like the name 'American' is not an ethnicity, neither is the name 'Christian""). In which case you are correct.
Under the OT Covenant, one was born naturally into Israel. Wild branches were even grafted in, if they converted under the Law. But even then they were in Christ, until one was cut off in unbelief. That is what being a natural branch afforded.
Jews are still naturally born into Israel.
What many of us fail to understand is that ever since God called Abraham and promised to be God to Abraham and his seed forever, the entire Bible is talking about God's elect nation,
and its ethnicity never mattered.
Abraham was a Gentile until he was called, and even after he was called, he was not a Jew. He was promised that he would become the father of many Gentile nations. It was God's first promise to Abraham which He repeated three times.
Abraham's son Isaac was not a Jew. Abraham's grandson Jacob, whom God renamed Israel, was not a Jew. Jews are the descendants of one of Jacob (Israel's) 12 sons.
Eleven of Israel's sons were not Jews, and all 12 sons and the tribes who descended from them were part of God's elect nation -
- until circa 725 B.C, when 10 of the tribes (except those of the Levites who were priests in Jerusalem, the Benjamites, and the Jews),
were broken off from God's elect nation, exiled from the land, and have never returned.
Within a couple of centuries all those who had been broken off from God's elect and exiled were not even called Israel anymore, because they had all become amalgamated with the Gentiles in the nations.
In circa 30 A.D all the rest of Israel - Levites, Jews, and Benjamites - who rejected Christ, who is THE promised seed of Abraham - were broken off from God's elect nation also,
but they did not believe (and still do not believe) that they had been broken off from God's elect nation, and they did not become amalgamated with the Gentiles in the nations, so they have always remained able to trace their genetic ancestry back to Jacob/Israel.
- - So they have continued to call themselves Israel AND be called Israel, just as did Paul.
This is the reason why those Jews, Benjamites and Levites who have remained broken off from God's elect nation are still called Israel, to this day.
The Jews are still natural branches of Israel. BUT NO ONE WAS EVER NATURALLY BORN PART OF GOD'S ELECT. It's impossible, because Abraham was elected because of his faith (belief in) God and in His Word - before he was even circumcised.
The name "Jew" is still synonymous with the name "Israel" purely because of ancestry, which creates
a lot of confusion. There is only ONE elect of God, and no one has to be born into Jacob/Israel in order to be part of God's elect, but all need to be born anew by the Spirit of God, being baptized into Christ by the same Spirit.