According to Paul, Peter feared “those of circumcision” (Galatians 2:12; Gr. tous ek peritomes). Elsewhere in the context, Paul speaks of those who are “of nations sinners” (2:15), “of works of the law” (2:16) and “of the faith of Christ” (2:16). Each time, Paul uses the proposition ek, out of.
Some of these could be simple identifying markers. Those “of” circumcision are simply those who are identified by circumcision. “Out of nations” may indicate no more than origin, perhaps even geography.
But I wonder if the preposition shouldn’t be taken more seriously. In essence, it means separation from, emission, exit. In some contexts, it is used with the verb “born” to describe the origin/nature from which something is born: “What is born ek flesh is flesh. What is born ek Spirit is Spirit” (John 3:6).
Might there be a birth image submerged in Paul’s usage? Jews are born of circumcision; they become Jews by circumcision of the flesh, and that which is born of flesh is flesh, and does the works of the flesh. That which is born of law cannot be justified, but only that which is born from the faith of (or by believing in) Jesus Christ.
Even without the “birth” idea, the idea of “emergence” or “emergence from a source” may be present. Origin determines nature, and Paul speaks of “natural” Jews, Gentiles who are sinners, people who emerge from law, people who have the nature that comes from originating from belief in/faith of Christ.