See related study - Israel of God - Is God "Finished" with Israel in His prophetic plan?

In 1847 the following article was published in Bibliotheca Sacra

The future condition of the Jews is a subject which has received from various sources no small attention. The subject is worthy of attention. It is worthy of attention for its own sake. Every branch of truth and every department of the divine operations has in it something to repay investigation. The connection of this subject with other themes imparts to it a still higher interest. The right understanding of it will lead to some views of essential importance in regard to the general character of the religion of the Bible, besides which some lessons of practical duty will grow out of it. The Jews have been a people greatly distinguished… In the investigation of this subject it is not a mere superficial view of it with which we should be satisfied. It is a subject which enters deeply into the economy of the gospel and involves principles of the very highest moment in the interpretation of the Bible.

THE ISRAEL OF GOD:
Has God Replaced Israel with the Church?
       Is the Church now "the Israel of God"?

In his last words to the Galatian believers Paul asked that "peace and mercy be upon them, and upon the Israel of God." (Galatians 6:16) A not uncommon misinterpretation (in my opinion) is to use this verse as justification for the hypothesis that since the majority of Jews rejected the Messiah and His gospel, God has instituted a new program in which the New Testament Church, the body of Christ, has replaced Israel and inherited the promises He originally intended to bestow on Israel. This genre of of teaching is often referred to as "replacement theology".  In context Paul is not using "the Israel of God" as a synonym for the church as is sadly taught even in evangelical works (eg, "The Disciple Study Bible" comments that now "The church is the true Israel.")

John MacArthur comments that...

The Israel of God refers to Jewish believers in Jesus Christ, to those who are spiritual as well as physical descendants of Abraham (Gal 3:7) and are heirs of promise rather than of law (Gal 3:18). They are the real Jews, the true Israel of faith, like those referred to in Romans 2:28, 29 (see notes) and Romans 9:6, 7 (notes). (MacArthur, J. Galatians. Chicago: Moody Press or Logos)

The highly respected conservative, evangelical Bible Knowledge Commentary agrees with Dr MacArthur's interpretation of (Galatians 6:16) writing that

The NIV errs in translating it "even to the Israel of God" rather than “and upon the Israel of God” as in the NASB. While some believe that “Israel of God” is the church, the evidence does not support such a conclusion. First, the repetition of the preposition (“upon” or “to”) indicates two groups are in view. Second, all the 65 other occurrences of the term “Israel” in the New Testament refer to Jews. It would thus be strange for Paul to use “Israel” here to mean Gentile Christians. Third, Paul elsewhere referred to two kinds of Israelites—believing Jews and unbelieving Jews (cf. Romans 9:6-note). Lest it be thought that Paul is anti-Semitic, he demonstrated by means of this benediction his deep love and concern for true Israel, that is, Jews who had come to Christ. (Walvoord, J. F., Zuck, R. B., et al: The Bible Knowledge Commentary. 1985. Victor or Logos) (Bolding added)

William MacDonald writes that...

Many have taken this (the phrase "the Israel of God") to mean the church. However, the Israel of God refers to those Jews by natural birth who accept the Lord Jesus as Messiah. There was neither peace nor mercy for those who walked under the law, but both are the portion of those in the new creation. (MacDonald, W & Farstad, A. Believer's Bible Commentary: Thomas Nelson or Logos) (Bolding added)

The King James Version Study Bible adds that...

The verse’s final and seems to distinguish between Gentile Christians (as many as walk) and Jewish Christians (the Israel of God). (Dobson, E G, Charles Feinberg, E Hindson, Woodrow Kroll, H L. Wilmington: KJV Bible Commentary: Nelson or Logos)

The Wycliffe Bible Commentary comments that while the "Israel of God" could possibly refer...

to the whole church, in view of the and, the more probable reference is to Christian Jews, such as Paul himself. These are the real Israel, as opposed to those who merely bear the name (cf. Romans 2:29-note). (Pfeiffer, C F: Wycliffe Bible Commentary. 1981. Moody or Logos)

Even older commentators such as Matthew Poole (1624–1679) have not seen the "church" in the phrase "the Israel of God", Poole commenting...

Upon the Israel of God, upon the true Israelites, whom he calleth the Israel of God hereby intimating and confirming the truth of what he had said, Romans 2:28, 29 (notes), and what our Saviour had said of Nathanael, John 1:47, calling him “:an Israelite indeed,” because in him was “:no guile;” and establishing a distinction between such as were so really, and those who were only Israelites in name, because descended from Jacob, to whom God gave the name of Israel. Hereby also checking the vanity of the Jews, who gloried in the name of Israelites, and thought there could no water come out of the fountains of Israel which God would cast away. The apostle doth not promise, or prophesy, mercy and peace to all Israelites, but only to the Israel of God; that is, to believers, that received and embraced Jesus Christ offered in the gospel." (Matthew Poole's Commentary on the New Testament) (Bolding added)

And of course the best "Commentator" on Scripture is always God Himself. Thus Jeremiah records Jehovah's testimony...

Behold, days are coming," declares the LORD, "when I will make a new covenant with the house of Israel and with the house of Judah, not like the covenant which I made with their fathers in the day I took them by the hand to bring them out of the land of Egypt, My covenant which they broke, although I was a husband to them," declares the LORD. But this is the covenant which I will make with the house of Israel after those days," declares the LORD, "I will put My law within them, and on their heart I will write it; and I will be their God, and they shall be My people. And they shall not teach again, each man his neighbor and each man his brother, saying, 'Know the LORD,' for they shall all know Me, from the least of them to the greatest of them," declares the LORD, "for I will forgive their iniquity, and their sin I will remember no more. Thus says the LORD, Who gives the sun for light by day, and the fixed order of the moon and the stars for light by night, Who stirs up the sea so that its waves roar; the LORD of Hosts is His name:

"If this fixed order departs from before Me," declares the LORD, "Then (When?) the offspring of Israel also shall cease from being a nation before Me forever." Thus says the LORD, "If the heavens above can be measured, and the foundations of the earth searched out below, then I will also cast off all the offspring of Israel for all that they have done," declares the LORD."  (Jeremiah 31:31, 32, 33, 34, 35, 36, 37) (Bolding added)

Beloved, Jehovah could not have been much clearer! God is not finished with Israel or the Jews! So continue to