The tragic irony in the book of Galatians is that those who are encouraging the new Christians to shore up their righteousness and their status as God's children by getting circumcised are actually directing them away from the only source of holiness.
In Galatians 6, the apostle Paul launches a last sally against these people, whom he regards as agitators. They are not genuine, he says; their concern is not real godliness, but just fleshly appearances and the avoidance of persecution. They do not keep the law themselves. (They perhaps did not consider themselves obligated to keep the whole law, but Paul sees the logic of their position: if you are making your righteousness dependent on things you've done, you'd better make sure you've done all the right things!) Paul has no interest in such a position. The cross of Christ means the death of that fleshly way of doing things. Neither circumcision nor uncircumcision count for anything, but only a new creation.
The point, I think, is that trying to seek righteousness by fleshly methods - by which Paul means anything that is driven by human effort or works, although obviously circumcision is a very literally 'fleshly' example! - is futile because the fundamental tendencies of the flesh are towards sin. Trying to get righteous using tools which are inherently biased against righteousness is pretty foolish. The cross of Jesus puts an end to it; he has done everything necessary, and we must trust in him.
But it seems that the question in Galatians is mainly about lived experience. How does the righteousness we're given by faith in Christ live its way out in daily experience? Surely at this point human effort has to come in?
Fundamentally the answer is no. Not that there isn't hard work involved, but it flows from the same Spirit who began the new creation in us. Since the Spirit gave us life, let's live in a way shaped and directed by the Spirit. And how is that Spirit given and received? Through the preaching and believing of the message of Christ.
So anything that takes us away from hearing and believing the message that Jesus alone is our righteousness also takes us away from the engine that drives practical, day to day godliness.