James and the other Jewish believers immediately point out that they still observe Judaism (zealous of the law).
So, they are Jewish believers and NOT believing Jews.
They valued their heritage above their faith in Christ.
Whereas Paul was demanding that the Gentiles forsake all their past religious beliefs to receive Christ Jesus as Saviour, Lord and King, the Jews were allowing, if not encouraging, Jewish believers to merely attach faith in Christ to their Judaism.
Paul has to address this error head-on in the book of Hebrews as, eventually, such Jewish believers would lose faith in Christ Jesus and His finished work.