Again, I don't believe that definition of "Israel" fits the biblical record, and is being imposed upon it by a particular NT theology. "Israel" has always been all Israel, believing or not. It is well known that Israel has always been at different stages of development and at different proportions of faith.
For example, how much faith was in Israel from the time they approached the Red Sea? I would suppose that most of them lacked faith to escape the Egyptians? However, many survived and crossed over. Later, many in Israel were pruned because of the rebellious kind of unbelief, but many others who lacked faith persevered and were less rebellious.
So lacking faith did not delegitimize portions of Israel--they remained part of Israel. And even if the whole nation fell into rebellious faith and were cut off from the land, being put into exile, the children of those same rebels were restored to the promised land.
Disagree. I think a strong case can be made that the unbelieving/non-observant among Israel were "not Israel" from the beginning.
Look at Matthew 13. Jesus explains the kingdom as a field of wheat and tares, planted together. We tend to focus on the end of the story... at the harvest, they will be sorted. The wheat goes in the barn. The tares go in the fire.
But look at the beginning... the idea here is that Israel was
planted as a mixed group. The enemy sowed tares at the same time the Lord sowed wheat.
In the same chapter, the kingdom is leaven hidden in flour. A treasure hidden in a field.
Look at 1st Kings 19 and Romans 11. Israel is already reckoned as a remnant, 7000 men who "have not bowed the knee to Baal," which exist, hidden, within the larger group of unfaithful. Paul says God hasn't abandoned Israel, and in the next breath he reckons Israel as
that remnant.
Look at Deuteronomy 11. Here at the very beginning of Israel, Moses divides the people into two groups. He put them on two hills facing each other, and gave them blessings and curses - the blessings for the faithful and the curses for the unfaithful.
The case is that "Israel" was always a mixed group - the faithful children of Promise
always existed alongside the reprobate. The former are truly Israel, the latter are a counterfeit Israel.