From that passage, in vs 21-24, did James believe that physical circumcision and keeping the Law, continue to be compulsory for the Israel of God?
Let's look at v.21-24
21 For the law of Moses has been preached in every city from the earliest times and is read in the synagogues on every Sabbath.”
22 Then the apostles and elders, with the whole church, decided to choose some of their own men and send them to Antioch with Paul and Barnabas. They chose Judas (called Barsabbas) and Silas, men who were leaders among the believers.
23 With them they sent the following letter: The apostles and elders, your brothers, To the Gentile believers in Antioch, Syria and Cilicia: Greetings.
24 We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said.
From this, the answer is no, obviously.
Yet in vs 25, did he exempt gentile believers from that, as originally stated in Acts 15?
Again, let's look at v.25-
25 So we all agreed to choose some men and send them to you with our dear friends Barnabas and Paul—
Nothing here about exempting anyone.
There is your distinction, that you refuse to see.
Except none of the verses that you have cited show anything of which you claim.
The whole issue in Actss 15 was that believers of the Pharisee party claimed that believers MUST BE circumcized to be saved.
v.1 - 1 Certain people came down from Judea to Antioch and were
teaching the believers: “Unless you are circumcised, according to the custom taught by Moses,
you cannot be saved.”
What followed was a clear statement that circumcision does NOT SAVE.
OK, after these comments I realized that you were quoting from Acts 21. But what I said from ch 15 are very important in this discussion, so I'm keeping my comments.
Now, for v.21-24
21 They have been informed that you teach all the Jews who live among the Gentiles to turn away from Moses, telling them not to circumcise their children or live according to our customs.
22 What shall we do? They will certainly hear that you have come,
23so do what we tell you. There are four men with us who have made a vow.
24 Take these men, join in their purification rites and pay their expenses, so that they can have their heads shaved. Then everyone will know there is no truth in these reports about you, but that you yourself are living in obedience to the law.
OK, Paul continued to live in obedience to the Law. So what? He sure didn't believe that the Law was part of what saved him.
Here's v.25 - 25 As for the Gentile believers, we have written to them our decision that they should abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality.”
These are rules for HEALTH. Physical health. The Law contains many beneficial rules for health. Like not eating pork, for example.
In the OT, poorly cooked pork would lead to serious health issues, like Trichinosis and such.
I STILL do not see anything that supports your supposed "distinction" between Gentile and Jewish believers.
If there are any such distinctions, you have not been able to show them.