If you remember, when the foreigners (strangers) came out of Egypt with Israel during the Exodus, we see three unique things happen.
1. They were to be treated as if native born. This means they were to be treated as if they were Israel.
2. The Torah was given to them as well, and they would be blessed if they kept it and cursed if they did not.
3. They were commanded to assimilate into the tribes they traveled with. In other words, they were grafted in....
If the covenant is made with only Judah and Israel... and that IS what the text says... then the believing gentiles who come in faith are simply grafted into Israel in the same manner gentiles coming out of Egypt were grafted in.
The word "gentile" was used in our first English bibles, it appeared like this "gentyls" in Tyndale's work, Wycliffe just used the word "hethene." Now when this word was used early in the English language, it meant heathen, pagan, anyone who wasn't a Jew or Christian (source, Webster 1828). But TODAY the word has evolved to mean, "any believer who is not Jewish." But that doesn't reflect the underlying Greek (ethnos) and Hebrew (goyim) which are best translated as nations, but any nation not Israel. What I am getting at is when we come in faith we cease being a gentile and should expect to be "treated as if native born." We have come to the God of Israel through the messiah of Israel and thus become a part of Israel. This is Paul's point in Eph. 2 where he says "you WERE gentiles in the flesh," and "WERE aliens of the Commonwealth of Israel" but "are NOW fellow citizens."
Truly in Scripture, a "gentile Christian" is an oxymoron... but in today's religious culture, it is a term worn as a badge of honor.