It helps to study, and know what the words Judah and Israel actually mean. There are many translations of these two words, unhappily many are more based on what the person using the translation has in mind, more than what the words actually mean.
I first investigated this in the 1960's and since I have alway made reference to many subsequent postulations on the words. It has become quite confusing since I first began due to the agenda's os so many folks tilting the meanings.
I am stisfied, evensince first studying this, but it will take study for others to be as I am, that is comfortble with my understanding that it is linguistic and not agenda driven.
When I say the Israel of God, or a Jew, I know what I uinderstand, but apparently the majority of others are thinking in terms of what is called Judaism today, also something that does not exist, for the Children of Israel, all the tribes, simply have or had the faith of Abraham. Allo sects under the uimbrell of Judaism arenotnecessarily the faith of Abraham, rather they are new denominations since the advent of our Lord. And so it goes with all denomination called Christian, for we too are adopted into the family of God, Yahweh, and we too are of the faith of Abraham. It is pointless to emphasize any denomination in lieu of the Word of God with the faith of Abraham, which even he received from God, just as we have.