From Calvin’s commentary on Galatians 6:16:
And upon the Israel of God. This is an indirect ridicule of the vain boasting of the false apostles, who vaunted of being the descendants of Abraham according to the flesh. There are two classes who bear this name, a pretended Israel, which appears to be so in the sight of men, — and the Israel of God. Circumcision was a disguise before men, but regeneration is a truth before God. In a word, he gives the appellation of the Israel of God to those whom he formerly denominated the children of Abraham by faith, (Galatians 3:29,) and thus includes all believers, whether Jews or Gentiles, who were united into one church. On the contrary, the name and lineage are the sole boast of Israel according to the flesh; and this led the apostle to argue in the Epistle to the Romans, that “they are not all Israel which are of Israel, neither because they are the seed of Abraham, are they all children.” (Romans 9:6, 7.)*
*Calvin, J. (1998). Galatians (electronic ed.). Calvin’s Commentaries (Ga 6:16). Albany, OR: Ages Software.