Rom 8:4,
That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
The crux of the new birth (Christians) is that God gave us holy spirit. It was a gift first given on the Day of Pentecost, 50 days after Jesus rose from the dead. It's in Acts chapter 2.
God made it pretty clear that the law made nobody righteous. On a whole, people simply are incapable of following the law of Moses by adhering to a list of do's and don'ts. However, Romans 8:4 (and many other verses) say we can fulfill the law by walking according to that holy spirit God gave us. What does walking by the spirit entail?
Rom 8:5,
For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
Walking by the spirit simple means to think, to mind the thoughts of God (contained in the scriptures) and not the world. The scriptures say God is love. The more we think about that the more we actually manifest that love. The scriptures further say that those who walk by love will cause no harm to their neighbor.
Rom 13:10,
Love worketh no ill to his neighbour: therefore love [is] the fulfilling of the law.
The word "love" is the Greek word "agape." It is part of the holy spirit God gave all Christians. It, like the gift of holy spirit, was not available in the OT.
I suppose there are some Christians who feel they can do whatever they want and the truth is they can. God didn't make Christian robots. Christians still have free will. Nonetheless I think it fair to say the vast majority of Christians are ready and willing to help their neighbor.