I am aware of Acts 21:20-25.
It was Paul's big mistake.
He should not have ignored the warnings in going to Jerusalem by the Spirit.
He dropped the ball and he was pressured to go through with an Old Testament purification rite that involved an animal sacrifice.
Anyways, according to BlueLetterBible, the epistle of James was written about 5 years after Acts 21 whereby Paul was shortly arrested after meeting with the Jewish apostles about the Law.
Source:
Acts and the Epistles Chronology - Study Resources
This lets us know that James would have known about Paul's writings. For does it not seem possible that James would counter argue against those who misunderstood Paul and twisted his words as Peter talks about in 2 Peter 3:15-16? For in 2 Peter 2, Peter refers to false teachers who have eyes full of adultery, and who cannot cease from sin (See: 2 Peter 2:1, and 2 Peter 2:14). It makes sense that James would be arguing the same thing at this point in the church's history.
Furthermore, Paul says there is no difference between Jew and Gentile (Romans 10:12).
Besides, Paul taught that we need to live holy and or we need to have works of faith (after being saved by God's grace) as a part of salvation, too.
“They profess that they know God; but in works they deny him, being abominable, and disobedient, and unto every good work reprobate." (Titus 1:16).
“...God hath from the beginning chosen you to salvation through sanctification of the Spirit and belief of the truth” (2 Thessalonians 2:13). Note: This is a call of the gospel (See: 2 Thessalonians 2:14).
“That they all might be damned who believed not the truth, but had pleasure in unrighteousness.” (2 Thessalonians 2:12).
For if ye live after the flesh, ye shall die: but if ye through the Spirit do mortify the deeds of the body, ye shall live.” (Romans 8:13).
“There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit.” (Romans 8:1).
"But unto them that are contentious, and do not obey the truth, but obey unrighteousness, indignation and wrath, Tribulation and anguish, upon every soul of man that doeth evil, of the Jew first, and also of the Gentile; But glory, honour, and peace, to every man that worketh good, to the Jew first, and also to the Gentile: For there is no respect of persons with God." (Romans 2:8-11).
19 "Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness,
20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies,
21 Envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God." (Galatians 5:19-21).
“For if God spared not the natural branches, take heed lest he also spare not thee. Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off.” (Romans 11:21-22).
"...work out your own salvation with fear and trembling." (Philippians 2:12).
“...And having become servants of God, ye have your fruit unto holiness and the end, everlasting life.” (Romans 6:22).
1 "This know also, that in the last days perilous times shall come.
2 For men shall be lovers of their own selves, covetous, boasters, proud, blasphemers, disobedient to parents, unthankful, unholy,
3 Without natural affection, trucebreakers, false accusers, incontinent, fierce, despisers of those that are good,
4 Traitors, heady, highminded, lovers of pleasures more than lovers of God;
5 Having a form of godliness, but denying the power thereof: from such turn away.
6 For of this sort are they which creep into houses, and lead captive silly women laden with sins, led away with divers lusts,
7 Ever learning, and never able to come to the knowledge of the truth.
8 Now as Jannes and Jambres withstood Moses, so do these also resist the truth: men of corrupt minds, reprobate concerning the faith.
9 But they shall proceed no further: for their folly shall be manifest unto all men, as theirs also was."
(2 Timothy 3:1-9).
11 “For the grace of God that bringeth salvation hath appeared to all men,
12 Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world;
13 Looking for that blessed hope, and the glorious appearing of the great God and our Saviour Jesus Christ;
14 Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works.” (Titus 2:11-14).