If the Jews were to hold on to the feasts and mosaic law, they, the Jewish Christians were told that it is not what saved them, it was the Grace of God that saved them.
St. James is having St. Paul and his companions shave their heads and such as not to offend the Jews in the Temple.
Paul is being a Jews to the Jews to convert them.
Just as he writes in his first letter the the Corinthians:
1 Corinthians 9:19-23.
For though I am free from all men, I have made myself a slave to all, that I might win the more. To the Jews I became as a Jew, in order to win Jews; to those under the law I became as one under the law – though not being myself under the law – that I might win those under the law. To those outside the law I became as one outside the law – not being without law toward God but under the law of Christ – that I might win those outside the law. To the weak I became weak, that I might win the weak. I have become all things to all men, that I might by all means save some. I do it all for the sake of the gospel, that I may share in its blessings.
If you go read St. Ignatius he talks about Christians turning to the Mosaic law and away from the Christian faith.
The Epistle of Ignatius to the Magnesians
Chapter 10. Beware of Judaizing.
Let us not, therefore, be insensible to His kindness. For were He to reward us according to our works, we should cease to be. Therefore, having become His disciples, let us learn to live according to the principles of Christianity. For whosoever is called by any other name besides this, is not of God. Lay aside, therefore, the evil, the old, the sour leaven, and be changed into the new leaven, which is Jesus Christ. Be salted in Him, lest any one among you should be corrupted, since by your savour you shall be convicted. It is absurd to profess Christ Jesus, and to Judaize. For Christianity did not embrace Judaism, but Judaism Christianity, that so every tongue which believes might be gathered together to God.
The Epistle of Ignatius to the Philadelphians
Chapter 6. Do not accept Judaism.
But if any one preach the Jewish law unto you, listen not to him. For it is better to hearken to Christian doctrine from a man who has been circumcised, than to Judaism from one uncircumcised. But if either of such persons do not speak concerning Jesus Christ, they are in my judgment but as monuments and sepulchres of the dead, upon which are written only the names of men. Flee therefore the wicked devices and snares of the prince of this world, lest at any time being conquered by his artifices, grow weak in your love. But be all joined together with an undivided heart. And I thank my God that I have a good conscience in respect to you, and that no one has it in his power to boast, either privately or publicly, that I have burdened any one either in much or in little. And I wish for all among whom I have spoken, that they may not possess that for a testimony against them.