You refer to a point that I often rethink but latelty I always get to a point where I accept both meanings side-by side, the notion of the Jews today, who say they are under the convenant even today and the notion of the RC church who says the church is body of christ, new people of god.
The church doesnt use as far as I know the term "Israelites" or "spiritual israelites" for the body of christ like Jehovas witnesses and perhaps other little similar theologians.
When Paul spoke about the olive tree, and used the picture to show that people of nations could be nourished from the abrahamic root, The olive tree is not the same as the "Israelites"
The usage of the term "israelite" for the body of christ I see as problematic. "people of God" okay, its a picture, that shows that in Christ all men shall become one people.
but there IS one "israel"...galatians 3:28.
In Galatians 3:28 Paul says that there is neither Jew nor Greek today in Christ, it doesnt say that it is one "israel".
This does not mean that all people of nations become Israelites, just as little as it means that all jews become Greek.
Instead of becoming part of Israel, Paul announces a new creature, the body of Christ that consists of two parts:
1. of Jews (Israelites) from the nations and circumcised, Christians and therefore "true beliefers"
2. and christians of nations.
What happens is that
The true believing Jews are becoming Part of the body of Christ
and not reverse that the body of Christ becomes part of the Jews or "a spiritual nation Israel".
15For neither circumcision nor uncircumcision means anything. What counts is a new creation.16Peace and mercy to all who walk by this rule,even to the Israel of God. 17From now on let no one cause me trouble, for I bear on my body the marks of Jesus.…
"Israel of God" here seems to refer not to all true believers, but to those believers from Israel who took refuge in Christ. The first sentence refers to beliefers of the nations, and the "israel of god" seem to be the the jewish saints not simple all Israelites according to the letter.
Instead of becoming part of Israel, Paul announces a new creature, the body of Christ.
“Having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace” –Ephesians 2:15
Out of two groups, Jews and Gentiles, Christ made a new man and agency for salvation. This special agency is what we become when we are saved today. We do not know any man after the flesh, whether it is Israel or American or European (2 Cor 5:16).
“Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new.” – 2 Cor 5:17
To think of being part of "spiritual Israel" is like always referring always to being part of nation after flesh nethertheless, like remainin in the "people" thinking.
whereas the body of christ is a new man, a spiritual body (not nation) . Therefore I dont like the term "spiritual Israel".
Some thoughts refer to the wegpage of graceambassadors fellowship http://graceambassadors.com/prophecy/israel/does-the-bible-teach-a-spiritual-israel )