The establishment of Law as basis for relationship with God was a major shift in perception in the ancient world, which had largely viewed the gods in highly anthropomorphic perceptions, acting on whims and emotions having only to do with their personal desires. For a fascinating study of a primitive mind working out such a projection, I recommend Browning's Caliban upon Setebos. To say that these are the things that please or displease God put the relationship on a much more secure footing. It should be no surprise that there are two major threads to these "Laws:" those which made for an orderly society, and those which established the priveleges and practices of the priestly class, who by some coincidence were the ones teaching the "Law."
Hebrew thought before Jesus was tending in the direction that it was really those social perceptions that were important to God and not the system of sacrifices and minor ordinances so important to the priests. Jesus' ministry and teaching was simply an extension of that, and a paradign shift from the importance of law for responsibility and order to the idea that the spirit that animated the idea of law, the concern for others as members of a whole society, is what is important in relating to God: fulfilling "law" as opposed to abolishing it.
When we operate in love, there is, for instance, no requirement for a law against murder. And, as noted, the law's requirement not to murder is really superficial in comparison to love's requirement that we not maintain anger against our brother. Therefore there are no "laws" that are a requirement, though such things may be set up for easy reference, each is subject to review as to whether it promotes a Way of love within our society. As Paul said in 1 Cor 10:23, " All things are lawful, but not all things are profitable. All things are lawful, but not all things edify." This is essentially the "New Covenant" prophesied by Jeremiah in which God's "laws" would be written on the hearts of those who operate in love. Our actions as well as our words will come from the abundance of our hearts.
Clearly the original disciples remained a part of the Jewish religion, and saw no conflict, though the attitude toward the priestly class and offices must have been quite different. That changed when Peter and Paul in particular started sharing the gospel with those who were not Jewish and the question arose as to whether those converts needed to convert to the Jewish faith, or only to the Way that Jesus taught, which was not confined to a faith tradition. The decision of the council was that they were not so required and their faith was able to operate outside of a religious tradition.
Unfortunately, the followers of the Way were not appreciated by orthodox Jews, particularly the leadership, and the whole group, Jew and gentile, began to have to operate outside a religious tradition until a new "clergy" or priesthood established itself and started constructing a religion around the Way taught and exemplified by Jesus. They didn't do so good.
One of the most interesting constructs has been the perception of "Atonement," and that perception is one of the cornerstones of the new "religion." The idea that Jesus somehow took away our culpability for failings when He was crucified is an essential part of the perception of Jesus as the founder and foundation of that system. How that worked is another problem entirely. There is a great (and short) review of some of the explanations that have been offered over the years, along with their attendant problems, in section II-the end of: http://www.quaker.org/quest/issue-9-gulley-01.htm and it is well worth a study.
My main point is that, with such a weak link as a foundational element, it has to be difficult to support the validity of the "religion" constructed with it. We have to wonder just how far past James' definition of "true religion" in James 1:27 we should depend on constructs and doctrines of men, and seriously examine the elements used in that construction.
However, for those who see beyond 2,000 years of that "religion" to the Way, it is indeed a "New Covenant" and consciousness concerning our relationship to God, our fellow humans and our world.