Being sin conscience is saying that Satan work in humanity was more effectual than what Christ has done in us, because it is a reminder of who we were before we were born again. One of the things God sought to do in our redemption was to eliminate the consciousness of sin because it brings about a sense of guilt, condemnation and inferiority. These characteristics are products of spiritual death which keeps us from entering God's presence, but since we have been born again there is now no condemnation (Rom 8:1), that is why God tells us to come boldly unto the throne of grace and obtain mercy and find grace to help in our time of need (Heb. 4:16).
Under the Old Covenant "It was not possible that the blood of bulls and goats should take away sin, because in those sacrifices there was a remembrance again of sins every year (Heb. 10: 3-4). We are under the New Covenant where Christ has appeared to put away sin by the sacrifice of himself (Heb. 9:26), and because of what Christ has done, Scripture says "This is the Covenant I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them, and there sins and iniquities will I remember no more (Heb. 10:16). So if God is not remembering your sin, why are you? "For by one offering he hath perfected forever them that are santified (Heb. 10:14).
People who are sincere about their faith in Christ do not make it a practice of sinning, but if they do it is not counted against them because we are holy and without blame in his sight (Eph. 1:2). This does not mean that because it is not counting against them one should continue to sin, what that does is give Satan place in their lives to bring about destruction because as you know he come to kill, steal and to destroy (John 10:10).