Remember Paul’s opening point: You do not stand “right” with God (righteous) because you are religious. Jewish Christians, depending on the religious nature of their Jewishness, believed they were okay with God. Paul’s point is that they are not.
It’s a huge point.
Jews depended on their Jewishness to confirm they were God’s people. But Paul says it doesn’t come that way. You must have faith. The proof that his Jewish readers (and gentile readers too) did not have faith (despite the fact they were Christians) was found in the way they lived their lives (note the lists of sins they are guilty of in 1:28 – 2:1 and 2:17 – 24). This is proof they do not have faith (3:3). It’s important you see Paul’s flow of thought. God has called us to an obedience that springs from faith because righteousness comes this kind of faith (the point in 1:1-17 – the last time Paul mentions “faith” until chapter three). Then, in the rest of chapter one and through chapter two, he describes what a life not characterized by faith looks like, and it looks like the lives of Jewish Christians who are counting on their Jewishness.
In chapter four, Paul focuses on Abraham. Though he was the father of the Jewish people, he did not stand right in the sight of God because he was Jewish, for God declared him righteous before he ever had the mark of Jewishness (circumcision). God declared him righteous simply because he “believed” God (had faith).
And how do we know he had faith?
Because he and Sarah continued to try and have children, despite the fact they were well past the age of being able to have children. This is often overlooked, as if because God promised they would have a child left them with nothing to do but wait for the pregnancy. But just waiting isn’t how a woman becomes pregnant.
Faith is an abiding trust in God that leads the believer to act as God directs. Without this obedience, faith is nonexistent, and so is righteousness.