"The Pharisaical "sect of the circumcision" believed that NO commandment of the Torah could be kept while uncircumcised in the flesh. Traditionally, the circumcised could not even enter the home of uncircumcised Gentiles."
I don't think this is an accurate assessment of Pharisaic beliefs. They actually taught that certain commandments of the Law were mandatory for the Nations to keep and they called these the Noahide Laws.
This is in regard to "believing" Pharisees, ones who have accepted Yeshua as Messiah. They were outraged that uncircumcised "believers" were keeping Torah in the diaspora while remaining uncircumcised. They took it upon themselves to 'initiate' believers into the Pharisaical sect of that time. Adult circumcision is how they "make proselytes". This was the same sect that Yeshua called hypocritical - meaning they were teaching the Law of Moses, not doing it themselves, while expecting their followers to do it perfectly.
The Noahide Movement began in the 12th century with Maimonides' interpretation of the Talmud. It became popular again as the modern "Noahide" movement.
https://en.wikipedia.org/wiki/Noahidism
I do not agree with the Noahide laws for Gentile interpretation, as the conclusion of Ecclesiasties states it's the whole duty of man (not just Israelite) to fear God and keep His commandments:
I also do not agree with the idea that the Acts 15 decision was James mandating "Noahide laws" for Gentile believers. It's a square peg in a round hole.
The laws given to Noah are good and righteous, but not complete. For example, in the future Gentiles will come to Jerusalem to keep the feast of Sukkot.
This is not included in the instructions given to Noah, but do pertain clearly to Gentiles (nations). The instruction for Sukkot are in the Torah. (Leviticus 23:34)