Christians Are Not Under the New Covenant

The Christian Church refers to itself as a 'New Covenant Church' believing that they are under the New Covenant. Many Churches have used 'New Covenant' for the name of their churches. Being under a 'New Covenant' implies that the previous covenant (the 'Old Covenant' or the 'Mosaic Covenant) has been replaced. The church identifies Jesus' shed blood as the means for initiating the New Covenant. But is that true? Since the Church figures it is no longer under the 'Old Covenant' it is no longer necessary to keep the laws of God for salvation. But is that true? Why did Jesus then tell us to keep them? These things we must study. If the church is wrong, it has led millions, perhaps billions of people astray. Is the church ushering them onto the Broad way which leads to destruction, while assuring them that they are on the road to eternal life and sing Christian hymns along the way?