The Gentile believers in the Diaspora were God-Fearing men who to varying degrees observed the Law of Moses. The issue that James is addressing specifically is adult circumcision:
But there rose up certain of the sect of the Pharisees which believe, saying that it was needful to circumcise them sending a message [for them] to also keep the law of Moses. (Acts 15:5)
The Pharisees viewed adult circumcision as joining their sect, people called 'those of the circumcision".
Now when Peter went up into Jerusalem, those of the circumcision contended with him saying 'You entered to men having uncircumcision and you ate with them.' Acts 11:2-3
The Pharisees made the claim that believers could not remain uncircumcised and also "keep the Law of Moses" even though only 8th day circumcision is mandated by Torah. Pharisaical conversion (adult circumcision) is what Peter calls the "yoke on the neck of the disciples which neither our fathers nor we are strong enough to bear." (Acts 15:10). Yeshua tells us that the scribes and the Pharisees "Bind heavy burdens, heavy and difficult to bear, and place them on men's shoulders" (Matthew 23:4)
We know that Peter does NOT referring the light yoke of the Torah (Matthew 11:30), since he refers to the righteousness of God (Torah) as equal to faith in Messiah!
"To them that have obtained an equally precious faith with us through the righteousness of God and our Savior Jesus Christ." (2 Peter 1:1)
James also writes that doing the Torah is a blessing:
"He who looks into the perfect Torah of freedom, and continues, he being not a forgetful hearer, but a doer of the work, this man shall be blessed in his deed." (James 1:25)
It's so easy to focus on the "no greater burden except these essentials" (Acts 15:20) as a Torah replacement for Christians and ignore the context where James explains "Moses, from ancient generations, city by city, has those who preach him, being read on every Sabbath in the Synagogues." (Acts 15:21)
So for us also, when Moses is read, city by city, may we not be a forgetful hearer, but a doer of the work! Be blessed!