The council at Jerusalem decided that believing Gentiles didn’t have the same burden as believing Jews, they all agreed on that. That was what was decided, not that believing Jews were relieved of any burdens, that wasn’t discussed. We don’t have a list of exactly what burdens a believing Jew had after the cross, only a list of what the Gentiles burdens were.
The Jews of true faith were not distracted from Christ by being burdened by the Old law that Christ had fulfilled through His crucifixion and resurrection. What do you believe this burden for Jews and not Gentiles was? The only burden (and I use that word because it's what you use) ALL people of faith have when they have been born again is to live our lives in faith of Christ, seeking to bring glory and honor to God in all that we speak and do. That's why there was this contention, not from Jewish Christians, but from Judaizers seeking to draw people away from the simplicity that is found in Christ.
We can surmise from Acts 21:21-22 that circumcision was a burden that the Jews had after the cross, because James calls out Paul on the issue in 59AD, 29 years after the cross.
As long as the Old Temple and city remained standing those calling themselves believers in Christ thinking they must still be obedient to the Law of Moses carried this burden not by necessity but by choice. Refusing to depart from the Old ceremonial and sacrificial laws and embrace the New Covenant through Christ continued until the destruction that likely brought death to many of them because they had not truly been converted to Christianity.
Whether we agree or disagree with the burdens of the Jews and what was happening during that time, we should at least admit it was taking place. We can say James should’ve told the Jews they weren’t under the burden of circumcision but instead he called out Paul’s preaching to the Jews about it, but we shouldn’t try to make it sound like these things never happened.
Yes, I agree that some Jews professing to be of Christ still continued to be burdened by the Old law. But according to Paul those who continued to believe that circumcision according to the law of Moses was still in effect after the advent of Christ were only Jews outwardly, making a show of the law, but inwardly they were not Jews of faith. Because Jews of faith understood true circumcision is not of the outward flesh but inwardly of the heart and that circumcision of the flesh was only profitable when they kept the WHOLE law.
Romans 2:25-29 (KJV) For circumcision verily profiteth, if thou keep the law: but if thou be a breaker of the law, thy circumcision is made uncircumcision. Therefore if the uncircumcision keep the righteousness of the law, shall not his uncircumcision be counted for circumcision? And shall not uncircumcision which is by nature, if it fulfil the law, judge thee, who by the letter and circumcision dost transgress the law? For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.