I don't see anything in the Bible that suggests that followers of Jesus obey the law automatically, otherwise the many commands and exhortations not to sin would be completely necessary. According to Titus 2:11-14, our salvation involves God's grace training us to follow what God has revealed to be godly, righteous, and good, and training us to renounce our doing what God has revealed to be ungodly, sinful, and lawless, and Jesus said that if we love him, then we will obey his commands (John 14:15), so there is no thinking about getting closer to salvation and Jesus without thinking about our obedience to the law. Paul said a number of times that we have become obedient slaves or servants of God (Romans 6:16, 1 Corinthians 7:22, Ephesians 6:6, Colossians 3:24, 1 Peter 2:16), so if we refuse to be mastered by God's law by grace through faith and the leading of the Spirit, then we defeat the purpose of our salvation. We are saved by grace through faith, not by doing good works, but for the purpose of coming into obedience to God's commands for how to do good works by grace through faith (Ephesians 2:8-10). Jesus set a perfect example of how to walk in obedience to the law and we are told to follow his example (1 Peter 2:21-22) and that that we ought to walk in the same way that he walked (1 John 2:3-6), so there is no such thing as following Jesus without following the law.