The entire letter is written to believers
Or do you think that the Scripture says in vain,"The Spirit who dwells in us yearns jealously? (
James 4:5)
James starts out by saying that he is a bond servant of Jesus Christ. He doesn't try to convert anyone in his entire letter, so I assume that the recipients were also servants of Christ. Why would he write to unbelieving Jews? He is obviously giving instructions for the
church.
In 2:1, he says "do not hold the faith of
our Lord Jesus Christ, the Lord of glory, with partiality." And then goes on to say how everyone who comes into the
assembly should be treated equally because God has chosen those rich in
faith (not possessions) to inherit the kingdom which "He promised to those who love Him". This is obviously the gospel that Christ preached to the Jews.
The whole tone is very Jewish and there is a lot written about the Law, so it seems clear that James wrote it to Jews, but they were believers in Christ.
Once again in verse 5:7 he uses the word brethren.