Ok, first off, you are making an assumption she was living with a man that was not her husband. The gospel does not indicate that other than she was caught in adultery so you are adding to the scriptures where that information is not there.
Secondly, homosexuals and adulterous were put to death under the OT, not liars or people having lustful thoughts. So to lump all those thing together is just bad theology. Sure having lustful thoughts is a sin but carrying those thoughts out is a whole other level.
Show me where in the early church found in the NT that people welcomed these people among them? I would like to see chapter and verse. But I will show you were these types of people were kicked out of the church and where people were very careful whom they let in. I am sorry but what you are describing is not only not biblical but frankly watered down gospel seeker friendly sinner coddling nonsense. It really is no wonder churches are full of fornicators, adulterers, homosexuals, drug addicts, and elders and pastors never address it but rather let it infect the whole body. You see if some guy is struggling with lustful thoughts and there is a woman who is sleeping with men in the church she calls her boyfriends from time to time don't you think that is really dangerous?
Sorry, I do not see this compromised version of embracing out right unrepentant sinners in the bible.
I will give a personal example. When my now wife and I were very new converts we were indeed living together, fornicating. I am so glad that the pastor told us to our face what we were doing. He did it in a loving way but showed us right in the bible where this was wrong. We repented, we got married and we stayed. I have no doubt if we did not repent, continued fornicating that the pastor would have asked us to leave and he would have been very right in doing so. To protect the flock. Now, I will say this, even though we repented we had things to deal with the Lord as a result of our actions that were tough to work through. Now if a church lets unrepentant homosexuals to just hang out, well you have a social club with a cross on the building and not a biblical church.....