The claim that Israel can only be those of the physical bloodline can be confusing. It is true that the New Testament does not say that those not of the bloodline who are the elect are Israel. But neither does it say they are not Israel. "Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ...... But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:
10.Which in time past were not a people, but are now the people of God: which had not obtained mercy, but now have obtained mercy." I Peter 2: 5, 9-10.
What did the prophecy in the Old Testament say? " And I will stretch over Jerusalem the line of Samaria, and the plummet of the house of Ahab: and I will wipe Jerusalem as a man wipeth a dish, wiping it, and turning it upside down." II Kings 21: 23
"Surely your turning of things upside down shall be esteemed as the potter's clay: for shall the work say of him that made it, He made me not? or shall the thing framed say of him that framed it, He had no understanding?" Isaiah 29: 16
"Arise, and go down to the potter's house, and there I will cause thee to hear my words.
3. Then I went down to the potter's house, and, behold, he wrought a work on the wheels.
4. And the vessel that he made of clay was marred in the hand of the potter: so he made it again another vessel, as seemed good to the potter to make it.
5. Then the word of the LORD came to me, saying,
6. O house of Israel, cannot I do with you as this potter? saith the LORD. Behold, as the clay is in the potter's hand, so are ye in mine hand, O house of Israel." Jeremiah 18: 2-6
God remade Old Covenant Israel. The Bible is not written like a grade school text book. Everything is not spelled out and repeated so the kiddies can easily get it without making some effort at understanding and having help from the Holy Spirit. Having everything spelled out over and over in an explicit way is called following the letter and not the Spirit in II Corinthians 3: 6.
I Peter 2: 5, 9 says God remade Old Covenant Israel as a spiritual house. Colossians 1: 26 says the riches of the glory of the mystery is Christ in you, the hope of glory.
The church is the same as ekklesia, the Greek word from which church is translated. It is the meeting, assembly or congregation of something that is more unique than just a meeting or assembly. You can call that unique thing the Body of Christ, the elect of God or even the saints. You can call it the Israel of God from Galatians 6: 16. Daniel 12: 3 says something about the elect of God, that they will shine as the brightness of the firmament.