The law of Christ is not the Mosaic laws the Jews were under.
The Law of Christ(1 Cor 9:21, Gal 6:2) is based on Loving God and Loving your neighbor (Mark 12:28-31). It is a moral law only.
Jesus told the scribe:
Love God with all your heart, all your strength all your understanding and to love your neighbor as yourself. This far exceeds the Mosaic law as in the old testament it was simply Love God and your neighbor. The law of Christ even includes the motives in our heart which the old testament never mentioned. Even more, we are to be led by the Holy Spirit (Gal 5:18)
The really cool thing about the 'law' of Christ is that the 'law of love' is not a law that we obey, but Fruit that we bear:
22 But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, 23 gentleness, self-control; against such things there is no law. 24 And those who belong to Christ Jesus have crucified the flesh with its passions and desires.
25 If we live by the Spirit, let us also keep in step with the Spirit.
And this is key:
16 But I say, walk by the Spirit, and you will not gratify the desires of the flesh. 17 For the desires of the flesh are against the Spirit, and the desires of the Spirit are against the flesh, for these are opposed to each other, to keep you from doing the things you want to do.
18 But if you are led by the Spirit, you are not under the law.
So the Scriptures say that if we walk by the Spirit, we will not gratify the desires of the flesh, and that if we are led by the Spirit, we are not under the Law.
In Romans chapters 5 and 7 we are told that the Law actually stirs up sin, so why would it make sense to try to live by that which stirs up sin?
There's a reason that God tells us we have died to the Law - it stirs up sin, results in dead works, and is the ministry of death (Rom. 5, 7, Heb. 6, 2 Cor. 3).
A better covenant built on better promises with a Perfect High Priesthood has been made available in Christ; to go back to the Old Covenantal system is spiritual adultery. (!)
-JGIG