Yes, I believe the dates are as close as we can get. My point being that James was the first New Testament letter written. I would not say it is outdated as it speaks to those he intended it for, and it certainly speaks to those today who say they have faith, but no works support their claim. To James the one who said he had faith, was the one who still observed the Law, but he had no works.
He had no revelation of the 'Church'. He had no understanding of both Jew and Gentile being formed into one Body. I doubt he had any knowledge of the Law being fulfilled or done away. When James writes he is writing to Jews who believe. (James 1:1-2) "...to the twelve tribes which are scattered abroad, greeting. My brethren...." See also, (1:18), and (2:1). And he no doubt was witness to and part of the coming of the Holy Spirit in (Acts 2). But this would be Jewish also. Fulfillment of prophecy to the Jews. Done on the day of the Feast of Pentecost. Affecting many of the 12 tribes of Israel who traveled to attend.
Now, I would agree with you that when James wrote he did not see the Gentiles as on equal ground with the Jews. Just as Christ acknowledged. (Matt. 15:26) Such understanding would not come until Paul's revelation from the risen Christ.
But I do not see this as making James outdated or making it not relevant for any Christian, both Jew and Gentile, even though it is Jewish in it's emphasis. All are always saved by faith. Faith always produces works. This is true before the Law, during the Law, and after the Law.
Yes, in (Acts 21) James still held to the Law for Jews. And for the Jew to abandon the Law would be for him wrong. As to exactly how much understanding he had at that time of the Law being done away, I don't know. But in (Acts 15) it was only the Law being placed upon Gentiles that he said was not necessary. And Paul never did argue the point at that time that neither was the Jew under Law anymore.
I personally believe both James and Paul were wrong in (Acts 21). And Paul would have been the more so as he had more revelation and knowledge of the Law being done away. I think both were doing it for the right reasons, but were wrong in the act.
I don't think I have answered anything. (James) is a difficult subject to say the least.
Stranger