All of us were blessed because we were born in a period where Scripture is complete, we can read both the OT and the NT together and truly understand how the grand plan of God is fulfilled.
But those who were living in the era of the 4 Gospels and Acts only had the OT, and thus, if I am a Jew living then, I would also have found Paul very difficult to understand and may even find him offensive. I grew up with the Law of Moses and have memorized the Torah front back and center.
Think of Acts as a transitional period where 2 messages of good news were valid at the same time, one for the Jews, another for the Gentiles.
Let me put myself in the shoes of a typical Judaizer, one of those who oppose Paul in Acts 15 and Galatians 1 and 2, to try to understand their objections to Paul:
The Jerusalem leaders are the only persons with authority to say what the true gospel is, and this authority they received direct from Christ. Paul has no comparable authority: any commission he exercises was derived by him from the Jerusalem leaders, and if he differs from them on the content or implications of the gospel, he is acting and teaching quite arbitrarily.
James was the brother of Jesus and lived with Jesus since he was a boy. The original 12 apostles were the only persons with authority to say what the true gospel is, and this authority they received direct from Christ when he was walking on Earth.
Thus, James was certainly correct when he was writing his book of James. He was taught by Jesus in the flesh, who said to keep the Law of Moses (Matt 5:19-20), to a young man who asked Jesus what must he do to gain eternal life, James may have overheard Jesus replying to "keep all the commandments" (Matt 19:17), and "sell all you have and give to the poor" (Matt 19:21).
Thus, we have to understand the book of James from that perspective. The book of James is like a throwback to the Sermon of the Mount.
Paul has no comparable authority. He claimed he got his gospel thru revelation from the ascended Christ in Gal 1
11 But I certify you, brethren, that the gospel which was preached of me is not after man.
12 For I neither received it of man, neither was I taught it, but by the revelation of Jesus Christ.
He further claimed that he spent 3 years in Arabia where he probably got those revelations directed from the ascended Christ himself.
15 But when it pleased God, who separated me from my mother's womb, and called me by his grace,
16 To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
17 Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
18 Then after three years I went up to Jerusalem to see Peter, and abode with him fifteen days.
19 But other of the apostles saw I none, save James the Lord's brother.
The Jerusalem leaders practiced circumcision and observed the law and the customs, but Paul struck on a line of his own, omitting circumcision and other ancient observances from the message he preached, and thus he betrayed his ancestral heritage. This law-free gospel has no authority but its own; he certainly did not receive it from the apostles, who disapprove of his course of action. Their disapproval was publicly shown on one occasion at Antioch, when there was a direct confrontation between Peter and him on the necessity of maintaining the Jewish food-laws.
Those are Paul's claims and no one else could verify the authenticity of his gospel. Why should I, as a Judaizer, believe him over the words of James and the original 12 apostles? As far as I know if Paul differs from them on the content or implications of the gospel, he is acting and teaching quite arbitrarily.
Now he is trying to preach that one can be saved without obeying the Law of Moses and that the Jews need not follow them. How dare he! (Acts 15 and Acts 21)