John Chrysostom

"For he is not a Jew which is one outwardly." Here he attacks them as doing all things for show.

Homily on Romans 6 ↗

Theophylact of Ohrid

Thus, he rebukes not circumcision (which he apparently respects), but the one who insults or transgresses it. Then, having proved this, he clearly defines who is a true Jew, and gives to understand that the Jews did everything out of vainglory. "For he is not a Jew," he says, "who is one outwardly, but he who is one inwardly," who does nothing in a merely sensory manner, but understands spiritually both the sabbaths, and the sacrifices, and the purifications.

Commentary on Romans ↗

Thomas Aquinas

Then when he says for he is not a Jew who is so outwardly, he assigns the reason for his statements. First, he gives the reason; second, he proves it, at whose praise. In regard to the first he does two things: first, he assigns the reason why circumcision or Judaism without observance of the law is fruitless; second, why observance of the law without Judaism and circumcision has value, at but he who is one inwardly. …

Commentary on Romans ↗