I understand the make up of the churches outside of Palestine were composed of both jews and gentiles and that legalism stemmed primarily from the jews not the gentiles so much (except for some Greek philophies).
However, what many on this forum seemingly do not understand is the significance of circumcision in this matter among the early Christians. As you know, with the exception of Abraham, circumcision occurred 8 days after birth and therefore it was the very first ceremonial ordinance experienced and was the public declaration at the beginning of committment to a LIFE OF LAW KEEPING. This is why the point was over circumcision in Acts 15, not so much to make gentiles Jews but to assert a committment to LAW KEEPING for the rest of their lives in order to be "saved" (justified).
This is precisely why Paul took circumcision back to Abraham instead of under Moses. If he would have taken any Post-Mosaic example he would have reaffirmed the doctrine of law keeping. However, in pre-Mosaic Abraham, who is also the father of circumcision there is a space of 14 years between the actual time he was justified by faith and the time he was circumcised. Also by declaring Abraham as the "father" (pattern) of ALL beleivers he was establishing the role of circumcision or any other ceremonial rite in the lives of true believers as to its value ("sign" or "seal") and yet denying it's role in obtaining justification by faith.
It is clear that the intent of circumcision by the Judiazers was to be the visible declaration that law keeping in addition to faith in Christ was necessary to be ultimately justified before God:
Ga 5:3
For I testify again to every man that is circumcised, that he is a debtor to do the whole law.
In Paul's use of Abraham in Romans 4:9-12 he totally repudiates the idea that circumcision can even be involved in justification by faith and therefore repudiates the whole theological system of justication by law keeping devised by the misinterpretation of circumcision by the jews.
The true design for circumicision is seen in Abraham as a "sign" or "seal" of an already justified state. Under Moses it is to be interpreted within the context of ceremonialism and symbolism. The infant being circumcised at eight days old is a symbol of the new birth under the New covenant rather than the literal means for new birth under the New covenant.
Paul puts literal circumcision in its proper place with literal justification by faith in the use of Abraham. In the Post-Mosaic use of circumcision it falls under the ceremonial laws of "shadow" and "symbol" and there literal circumcision of literal babies is a type of the new birth under the new covenant.
In properly placing circumcision in the context of Abraham, justification BEFORE circumcision Paul with one blow shatters the whole Legal system and gospel of Christ perpetuated by the Judiazers which made circumcision the first step toward justification through the works of the law which is the very same idea incorporated into Roman Catholicism as they view baptism as a means to convey new birth and justification.
To be fair specifically judaism. Since it was common for the Jews to require imposition of the Law on the new gentile believers. Note remember Judaism doesn't just purport the Mosaic law. But it holds all gentiles to Nohide laws and Abrahamic laws to the Jews.