I won't comment on the rest of your dialogue; but, I will say this. The new covenant requires obediance every bit as much as the old. If you're of the notion that obediance went out the door and we can all be jolly and dance forth in ignorance of God's requirements, you need to get yourself into a concordance and look up the iterations of the word obey and disobey and check all the mentions in the NT. You'll find that eternal life as a promise is hinged upon the notion and that our very name of Christian derives from being not merely hearers but doers - listening and being obedient to the leading of the spirit. (John 10, Romans 8, Acts 5, Mark 16...)
No, the category of obedience is incorrect. The New Covenant requires love which is willing to follow Jesus through the empowerment of the Holy Spirit.