The two conflicting doctrines would be "Justification by Faith" and the Calvinist doctrine of "Predestination" These two doctrines are in conflict with each other. If you have been predestinated to salvation by God before the foundation of the world then you don't need to be justified by faith. If God declared that you are saved before the foundation of the world, then there is nothing else needed to secure your salvation, not faith, not belief, not works, nothing, absolutely nothing. I would go so far to say that not even the Christian life.
Some Calvinist say that God gives those that have been predestinated faith to believe the Gospel. Truth of the matter is, is that we are all born with faith. It is a natural human attribute. As a child we have faith in our parents and then we marry and have faith in our spouse. When we hear and believe the Gospel that same faith is directed towards Jesus Christ. This is what Paul meant when he said... "Therefore being justified by faith (made right with God) we have peace with God through our Lord Jesus Christ" Romans 5:1. We have peace with God because we are Justified by the doing and the dying of Jesus. Jesus is our justifier, Romans 3:26. The righteousness of God is to our account, Romans 3:22.
No, Paul did not preach two conflicting doctrines. There is no scripture in the Bible that says anyone has been predestinated to heaven or to hell. If predestination to salvation was a correct doctrine the New Testament would be full of it. The word is only found four times in the New Testament and is totally absent in the Old Testament. The Old Testament saints were justified by faith in God's promise of a savior. Things have not changed. We are also justified by faith. They looked forward to the realization of God's promise of a savior. We look back to when he was here and are justified by faith.