They rose up against Paul, accusing him of inducing people to worship God contrary to the law. Paul was well versed in Jewish law and doctrine and was an expert in the worship proper to God. We know that he was zealous in the teaching of proper doctrine. However, after his encounter with Jesus, he realized that his zeal fell short of worship proper to God and then proceeded to make up for his former way of life by proclaiming the risen Christ (cf. Acts 22:1-21). The same zeal with which he had persecuted the Christians was now employed in service to the teachings of Christ. Whereas we are not told of the particular contents of Paul’s teaching that was seen as contrary to the [Jewish] law, we can presume that it all had to do with the new worship proper to God that had been made possible in Jesus Christ and whose fierce preacher Paul had become. 
The “older” worship was for the most part external and emphasized the vertical relationship (with God) at the expense of the horizontal one (with fellow human beings). The “older” form of worship was structured in a way that made it more cosmetic. It was more of an external display that did not lead to inner transformation. It is this kind of worship that Jesus had condemned (these people worship me with their lips but their hearts are far from me [cf. Mark 7:1ff]). The new worship “introduced” and promoted by Jesus is holistic and allows the one making it to achieve a transformation that moves him/her closer to attaining eternal life with God. It is about this “proper” worship due God that Paul might have been reminding his fellow Jews.
A proper worship of God must make the transition from external to the internal. A worship due God must be both vertical and horizontal, that is, one must ascend to God through the neighbor for we can love God only by loving our brothers and sisters (cf. I John 4:20). The “older worship” never included one’s neighbor. It was okay to focus on establishing and maintaining a healthy relationship with God while paying minimal attention to one’s neighbor. In the “older” worship, it was okay for one to disregard the plight of one’s fellows yet still be in perfect relationship with God. Although practiced for generations, it was found wanting. The perfect worship due to God has been revealed in Jesus Christ, and it begins by loving one’s fellows for this is the ladder through which one ascends to God.