There you are in your normal seat just before worship begins. In walk two people, visitors, and seeing a couple of empty chairs next to you, they sit. As the service progresses it's clear that they aren't used to church. So, you help them find the right pages for the hymns and Bible readings and that sort of thing. After worship you chat and find out that God seems to be at work in their lives. It has become clear to them that life is not working. While neither of them grew up in families with any sort of religion, one of them had an old grandmother who used to talk about church. So, on a whim, they chose to visit your church. They tell you that they didn't understand most of what was going on, but they want to come back. Something feels right to them about what the pastor was talking about. At that point you tell them about the monthly luncheon that will start in a few minutes and invite them to stay. They are grateful and accept the offer. All the while you're thinking about developing a relationship with these two people so that over time they can come to know Jesus as Savior and Lord. They know absolutely nothing about the Gospel, but they seem so open to listen. You're hoping (and praying) that the Spirit will work and two more will bow before Jesus.
All of that is to get to this. Does it matter what their particular set of sins is? Are there certain kinds of sin that they have to jettison first, before you are willing to befriend them? Are you willing to reach out to them if their particular sins have to do with compulsive gambling? What if they're lazy or greedy? I suspect that your average Christian is able to overlook those sorts of sins in the hope that he might establish a friendship that leads to the eternal rescue of these clueless sinners. But I also suspect that your average Christian would not be able to overlook their sins if they were in any way related to sex. Why is that?