Sincerity is not what saves people. Only the sacrifice of Christ, and trusting in what he has done on the cross, can save a person from the righteous judgment of God. Galatians 2:21 says "If righteousness comes by the law, then Christ died needlessly." In other words, making us righteous before God is not by our effort, or sincerity. It's by the work of God himself in the person of Christ on the cross.
Also, appealing to sincerity is an appeal to what is in the person; that is, it is an appeal to some so-called good quality (sincerity) in someone. But this would mean that God was showing favoritism based upon what was in the person. God does not do this (Rom. 2:11). Besides, the Bible says that our hearts are desperately wicked and deceitful (Jeremiah 17:9) and that no one does good (Romans 3:12). So, sincerity can never be good enough to warrant forgiveness of sins. This is why everyone needs the gospel of Jesus.