I don't think he is placing these up as new equivalents for circumcision. Rather I think he is now describing some matters that will be important in the fellowship of Jewish and Gentile Christians. You will reflect on this more next week. Outside the church there is no salvation. This passage, along with Galatians and Ephesians 2, affirms that salvation is a sheer gift.
Salvation comes with the entrance of the Holy Spirit in our lives.
Holy Spirit will bring a purifying source, but that comes with the deposit of grace. So many are not sure. We have come through an era of Christendom when everyone thought they were Christian. A Christian is someone who has received Jesus Christ, and invited the Holy Spirit into their life. A Christian is not someone who knows the Bible particularly well.