The imputed righteousness of Christ is not only in having a belief in Jesus, but it also involves works of faith, too. For the imputed righteousness of Christ continues to work in our lives if we also walk in the light as He is in the light.
"But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin." (1 John 1:7).
Walking in the light = Keeping God's commandments
(or loving your brother) (Compare 1 John 1:5-7 with 1 John 2:3-4 and 1 John 2:10-11).
Some are saying that they are sinners and that they can break God's Moral Laws on some level (i.e. not walking in the light) and yet, they are still be saved. While some of them say that they do not live in a lifestyle of sin, they preach a double message (and contradict themselves), and say that a believer sins all the time or they cannot keep all of God's laws. However, 1 John 2:4 says that the person who says they know God and does not keep His commandments is a liar and the truth is not in them.
For after a person accepts, Christ, grievous sin can still separate them from God unless they repent (seek forgiveness with God - 1 John 1:9) and then fruits of repentance (deeds) (forsaking sin and good works) shows that their repentance is true (1 John 1:7). Adam's one sin caused a separation between all of mankind and God (1 Corinthians 15:22). Peter told Simon to repent of his one sin of trying to pay for the Spirit by praying to God with the hope that he may be forgiven of him (Acts of the Apostles 8:22). Ananias and Sapphira died over each of them committing the one sin of lying to the Holy Ghost; And a great fear came upon the church and all who heard it (See Acts of the Apostles 5:1-11). Why would the church fear God if Ananias and Sapphira were saved?