Very important question and matter... Let us see how we can think about it:
Unbeliever_A is a person of the world, he loves and commits many of the sins we see nowadays in this world, many of these sins which are considered part of the world, are fully tolerated and accepted as a normal activities by its society.
Obviously, just because those "activities" are considered normal and acceptable by the world it does not mean they will not be seen by God as a sin or an abomination. Because what is an abomination will always be considered an abomination, the world can change but God will never.
Unbeliever_A goes to church, learns about the Word of God, learns about Jesus' story and teachings, he knows about Jesus and decides to accept him as his Lord and Savior. He now is Believer_A from now on.
Eventually, Believer_A learns the activities enjoyed and practiced by Unbeliever_A were condemned by his Lord and Savior, Jesus Christ. Believer_A understands it and now sees it, and decides to act accordingly his Lord, Jesus Christ.
Believer_A is now focused and stays in vigilance with the Word of God in his heart, so he won't sin against his Lord Jesus Christ, and His Father. Believer_A is no more willing to fulfill the desires of his flesh, but the will of the Father who is in heaven.
We can safely say Believer_A is doing a great job, and his Lord, Jesus Christ is very happy of his effort to walk on the right path. Although Believer_A makes every effort to stay on the right path, he eventually fail in some circumstances, but not because he willfully wished to do so, he learns of his fail and immediately run to his Lord in signal of repentance.
Believer_A is not interested in the things Unbeliever_A was so focused into anymore.
We can say Believer_A is now truly changed, a new creature, he definitely was born again, and now he is in Christ:
"Therefore, if anyone is in Christ, he is a new creation; old things have passed away; behold, all things have become new. - 2 Corinthians 5:17"
God bless us all, and that all our desires be His desires... Let us forget the things of the world, and focus on what really matters: The Will of God.
Thank you, God! All the glory to God.