You are far wide of the mark in your claims about Christians and the Law.

Christians (saved by Grace apart from the Law) do not keep the Law by merely not stealing. They fulfill the Law by doing the opposite, by giving and helping those in need.

Christians do not keep the Law by not killing. They fulfill it by promoting even the life of their enemy.

Christian do not keep the Law by not coveting. They fulfill it by blessing their neighbor and working for his or her well being as if it were their own.

And so on. The entire New Testament system of ethics is based on fulfilling the Law by doing the opposite of what it forbids, not just "keeping" it as the Pharisees were so good at.