This statement is saying that being ethnic Israel, is necessary, but not sufficient, to be true Israel
Which is also saying that you cannot be true Israel, if you are not ethnic Israel.
Right. That's exactly what I was saying, that to be true to what Israel was called to be one must live by the Law of God for Israel. Otherwise, they would not become non-Israel. Rather, they would become *as if* they were not Israel, and would be cut off or sent away into exile, out of their land.
Hosea 1.6 Gomer conceived again and gave birth to a daughter. Then the Lord said to Hosea, “Call her Lo-Ruhamah (which means “not loved”), for I will no longer show love to Israel, that I should at all forgive them. 7 Yet I will show love to Judah; and I will save them—not by bow, sword or battle, or by horses and horsemen, but I, the Lord their God, will save them.”
8 After she had weaned Lo-Ruhamah, Gomer had another son. 9 Then the Lord said, “Call him Lo-Ammi (which means “not my people”), for you are not my people, and I am not your God.
The sad truth in history is that the Northern Kingdom, who had abandoned their God in Jerusalem, and created false gods, were sent away by God into exile. And they ceased being "Israel" quite literally by merging in with their captive nation or with other nations, together with their gods.
But the Southern Kingdom, who worshiped their God rightfully in Jerusalem, even when they were sent away into exile for their sins, were able to return. They retained the title of "Israel," and represented all 12 tribes there, since many from the Northern Kingdom had migrated there to be with them.
Thus, not all who had been part of "Israel" would retain their title if they did not remain faithful to God's Law. They could be cut off and sent away, to merge with other pagan nations. This had nothing to do with calling any Jew "non-Israel." It was their choice to leave Israel that caused them to lose their status.