There is some evidence that during the intertestamental period at least some Jews thought that circumcision was required for a convert to Judaism. In Josephus Antiquities 20.2.4 we read the story of Helena, queen of Adiabene, and her son Izates, who “changed their course of life, and embraced the Jewish customs.”
What is interesting here is that Izates desires zealously to embrace Judaism, and decides to be circumcised. Helena and the Jewish Ananias tries to dissuade him on the grounds that he is a king, and the people will not accept the rule of a king that practices a foreign religion. Ananias seems to be arguing that if there is a mortal danger, circumcision can be ignored (if the person as a hemophiliac, for example.) Since allowing himself to be circumcised might lead to the rebellion of his people and the loss of his and his family’s life, Ananias recommends that he not be circumcised. After Izates decides to forgo circumcision, another Jew Eleazar, described as being “extremely strict” with respect to the Law, tells Izates that he is breaking the Law if he does not submit to circumcision. Izates does immediately receive circumcision, and Josephus tells us that God preserves him in the dangers he faces later in life because he obeyed the Law fully!
In the Loeb Edition of Josephus there is a lengthy footnote on this story. A few scholars have drawn attention to the fact that the debate between Ananias and Eleazar reflects the two schools of rabbinic thought in the first century, that of Hillel and Shammai, with respect to circumcision. In Talmud Yebamot 46 a there is a description of a Rabbi Joshua who taught that only baptism was necessary for a Gentile convert, and the Rabbi Eleazar who argued that circumcision was necessary for the Gentile convert. J. Klausner argued that the dichotomy between Joshua and Eleazar is similar to that of Paul/Barnabas and Peter/James (as suggested by Klausner), but this may be reading the Paul / Peter relationship as a strict dichotomy alá Bauer.
Does the story of Izates indicate that Hellenistic Jews were more liberal on circumcision than Palestinian Jews? Assuming that Ananias is a Hellenistic Jew and Eleazar is a Palestinian Jew, Schiffman (127) notes that the argument has been made that Hellenistic Jews did not require circumcision. But this is not the case since Ananias never argues that circumcision for a convert is not required, but that in this case there is an acceptable and legal “out” of Izates that will perhaps preserve his life. Josephus’ comments at the end of the story make it clear that he approves of Izates’ decision to be circumcised. This brief survey indicates that the practice of circumcision was one of the most important issues to Jews of the first century. Even for a Gentile convert, circumcision was required in order to be part of the “people of God.”
Does this story from Josephus help illustrate what is at stake in Acts 15 and Galatians?
Bibliography: Schiffman in Jewish and Christian Self-Definition Volume 2 (Philadelphia: Fortress, 1981), 115-156, especially 125-127; J. Klausner, From Jesus to Paul (1943), 39-40.

