"When I saw that they were not acting in line with the truth of the gospel, I said to Peter in front of them all, 'You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs?'" NIV translation
Paul publicly corrected Peter with a question. Basically, Paul asked how Peter could enjoy the freedom that he has in Jesus Christ and yet deny that freedom and in fact try to put the Gentiles back to bondage of the law. This may seem harsh but the same question could and should be asked to many "religious leaders" today.
"'We who are Jews by birth and not "Gentile sinners" know that a man is not justified by observing the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by observing the law, because by observing the law no one will be justified.'" NIV translation
Three times, in this passage, Paul reminds Peter and us as well that it is only by faith in Jesus that we are made right with God. There is only one way for anyone to be saved and that always was and always will be through the blood of Jesus.
There are no exceptions as all have sinned and fallen short of the glory of God. This is the same message that Paul shared in his letter to the Romans.
"'If, while we seek to be justified in Christ, it becomes evident that we ourselves are sinners, does that mean that Christ promotes sin? Absolutely not!'" NIV translation
We are made right with God through the blood of Christ but we still live in sinful world. Jesus loves us but He does not promote sin and wants us to live free from the effects of sin. This process is called sanctification and is a work of the Holy Spirit.
"'If I rebuild what I destroyed, I prove that I am a lawbreaker. For through the law I died to the law so that I might live for God. I have been crucified with Christ and I no longer live, but Christ lives in me.'" NIV translation
Jesus kept the law perfectly and was therefore the perfect sacrifice for our sins. Through Him, we die to the law and are no longer under law but are under grace. When we accept that gift of grace, the old self is crucified and we are a new creation with Christ living in us.