Paul said we must examine ourselves if we are in the faith. What need is there to examine ourselves if there is no such thing as false faith.
If faith saves us, and it does, then the command to examine ourselves to see if we are in the faith means that it is possible to have a false confession.
James is dealing with the issue of those that MAY have a false confession.
Interesting points you raised.
Maybe the point here is confession.
As Paul says
Romans 10:9-13
9 that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. 10 For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. 11 For the Scripture says, “Whoever believes on Him will not be put to shame.” 12 For there is no distinction between Jew and Greek, for the same Lord over all is rich to all who call upon Him. 13 For “whoever calls on the name of the Lord shall be saved.”
The crunch here is V9 mainly being Lord and raised from death.
Over here their are people who go to church because it's the thing you do as we are a Christian country (culture). Then we have those who consider themselves Christian because of the culture.
Not had lots but a few occasions when I have wondered if in fact they are Christian or as I say "Followers of Jesus" I quote verse 9. Alas they fall foul of that. Mainly on the basis of being raised from the dead.
That being the case then he is not Lord and it's a false confession.
Sadly I have had to refuse baptism for 2 people who refused to confess that they believe Jesus rose again.