What the Bible takes seriously we take seriously. When you find something over and over again, constantly being emphasized to multiple groups of people by the inspired authors of scripture it is important to pay attention.The New Testament writers both emphasized the power of God's grace and the power of sin. The first one triumphs over the second but it doesn't mean the second becomes unimportant. The second is important and should get our attention for the very reason that it is something God is triumphing over, therefore, we should have nothing to do with it. If God is battling something, let us be on His side not the side of the enemy.When Paul talks about Jesus taking care of our sin, he also makes sure to emphasize that we don't, as a result, get careless about sin. We see that if we reconnect Romans 5 and 6 as Paul initially penned them without chapter breaks,

¹⁸ Therefore just as one man’s trespass led to condemnation for all, so one man’s act of righteousness leads to justification and life for all. ¹⁹ For just as by the one man’s disobedience the many were made sinners, so by the one man’s obedience the many will be made righteous. ²⁰ But law came in, with the result that the trespass multiplied; but where sin increased, grace abounded all the more, ²¹ so that, just as sin exercised dominion in death, so grace might also exercise dominion through justification leading to eternal life through Jesus Christ our Lord.

What then are we to say? Should we continue in sin in order that grace may abound? ² By no means! How can we who died to sin go on living in it? ³ Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? ⁴ Therefore we have been buried with him by baptism into death, so that, just as Christ was raised from the dead by the glory of the Father, so we too might walk in newness of life.

⁵ For if we have been united with him in a death like his, we will certainly be united with him in a resurrection like his. ⁶ We know that our old self was crucified with him so that the body of sin might be destroyed, and we might no longer be enslaved to sin. ⁷ For whoever has died is freed from sin. ⁸ But if we have died with Christ, we believe that we will also live with him. ⁹ We know that Christ, being raised from the dead, will never die again; death no longer has dominion over him. ¹⁰ The death he died, he died to sin, once for all; but the life he lives, he lives to God. ¹¹ So you also must consider yourselves dead to sin and alive to God in Christ Jesus. (Rom 5:18-6:11)

Here you see the seriousness of sin that still exists even though God is working to make us righteous in spite of our sin. It would be like the dad who cosigned the loan with his son and realized he was going to have to pay off the whole thing. Coming to peace with the reality, the father pays the debt in full only to find out that his son has gone out and borrowed from a dozen other lenders. How frustrating. The son should know by now that he couldn't pay the first one. No good, respectful, loving son would want to continue to put his father in such a position. But one who is manipulative and selfish and uncaring would do just that, gaining more for himself at his father's expense...anticipating the bail out.Let us understand that BOTH our sins are taking care of by God through Christ AND that our sins are still deadly serious.Go and sin no more, trusting God will take care of our failures along the way. Grace doesn't make obedience unnecessary. Grace makes obedience the logical and natural response.