In the story of Zacchaeus (found in Luke 19:1-10) we see a great example of how Jesus dealt with those that obviously were living in sin.
Here is what it says:
"Jesus entered Jericho and was passing through. A man was there by the name of Zacchaeus; he was a chief tax collector and was wealthy. He wanted to see who Jesus was, but because he was short he could not see over the crowd. So he ran ahead and climbed a sycamore-fig tree to see him, since Jesus was coming that way.
When Jesus reached the spot, he looked up and said to him, “Zacchaeus, come down immediately. I must stay at your house today.” So he came down at once and welcomed him gladly.
All the people saw this and began to mutter, “He has gone to be the guest of a sinner.”
But Zacchaeus stood up and said to the Lord, “Look, Lord! Here and now I give half of my possessions to the poor, and if I have cheated anybody out of anything, I will pay back four times the amount.”
Jesus said to him, “Today salvation has come to this house, because this man, too, is a son of Abraham. For the Son of Man came to seek and to save the lost.”
Jesus came to seek and save the lost. He didn't avoid them nor did he condone what they were doing. I think that is an important example for our lives too. We shouldn't avoid those that are struggling with sin (because we all do that - though some sins are more obvious than others) but we shouldn't pretend that sin is okay either. We need to work to teach and encourage being right with God whenever we have the opportunity. Jesus was aware of opportunities like this and took advantage of them.
I hope I can do the same.
Something else we can learn from this story is just how Jesus gives grace - to you, to me, to whoever wants it! I am so grateful for God's grace!