I think it's fine to call them "Christians" (after all, they will indeed be believers in Christ / their Messiah, at that point)... I just believe they are never called "the Church WHICH IS HIS BODY" (and that Eph1:10 is not speaking of "in this present age [singular]," but that awaits a future time--unlike the rest of the epistle which IS speaking of "this present age" [the 'one new man' etc; where there is neither Jew or Gentile in our standing before God IN CHRIST])
Should we say Jesus, his twelve disciples turned apostles, the apostle Paul, and all of the early solely Jewish church, before the apostle Paul went to the Gentiles, were to be called part of His church? Christ Yeshua instituted His church, Body of Christ, God's restored chosen Christian people:
Matthew 16 (New King James Version)
18And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not
[g]prevail against it.
John 11 (New King James Version)
49And one of them, Caiaphas, being high priest that year, said to them, “You know nothing at all,
50nor do you consider that it is expedient for
[e]us that one man should die for the people, and not that the whole nation should perish.”
51Now this he did not say on his own
authority; but being high priest that year he prophesied that Jesus would die for the nation,
52and not for that nation only, but also
that He would gather together in one the children of God who were scattered abroad.
53Then, from that day on, they plotted to put Him to death.
54Therefore Jesus no longer walked openly among the
Jews, but went from there into the country near the wilderness, to a city called
Ephraim, and there remained with His disciples.
The restored Kingdom of Israel will be a continuation of the work Christ Yeshua started in his Body of Christ believers, God's chosen people, the Christians of which believing Israel will be part of, along all other believing peoples of all tribes, tongues and nations - but Israel is not a separate chosen people from God's Christians. Israel will however be God's Christians residing in Israel when Christ Yeshua resides in Jerusalem during His millennial Kingdom reign here on earth, whilst believing Christian peoples from all tribes and tongues and nations will be residing all over earth during Christ Yeshua's millennial Kingdom reign here on earth. We are however in for a surprise on who all were from Israel, as Israel's Ephraim tribes is still scattered without identity among the Gentile nations.
Acts 1 (New King James Version)
5for John truly baptized with water, but you shall be baptized with the Holy Spirit not many days from now.”
6Therefore, when they had come together, they asked Him, saying, “Lord, will You at this time restore the kingdom to Israel?”
7And He said to them, “It is not for you to know times or seasons which the Father has put in His own authority.
8But you shall receive power when the Holy Spirit has come upon you; and you shall be
[c]witnesses to Me in Jerusalem, and in all Judea and Samaria, and to the end of the earth.”
Revelation 20 (New King James Version)
4And I saw thrones, and they sat on them, and judgment was committed to them. Then
I saw the souls of those who had been beheaded for their witness to Jesus and for the word of God, who had not worshiped the beast or his image, and had not received
his mark on their foreheads or on their hands. And they lived and reigned with Christ for
[a]a thousand years.
5But the rest of the dead did not live again until the thousand years were finished. This
is the first resurrection.
6Blessed and holy
is he who has part in the first resurrection. Over such the second death has no power, but they shall be priests of God and of Christ, and shall reign with Him a thousand years.
Ezekiel 37 (New King James Version)
14I will put My Spirit in you, and you shall live, and I will place you in your own land. Then you shall know that I, the Lord, have spoken
it and performed
it,” says the Lord.’ ” .
25Then they shall dwell in the land that I have given to Jacob My servant, where your fathers dwelt; and they shall dwell there, they, their children, and their children’s children, forever; and
My servant David shall be their prince forever. 26Moreover I will
[c]make a covenant of peace with them, and it shall be an everlasting covenant with them; I will establish them and multiply them, and
I will set My sanctuary in their midst forevermore.
Isaiah 66 (New King James Version)
23And it shall come to pass
That from one New Moon to another,
And from one Sabbath to another,
All flesh shall come to worship before Me,” says the Lord.