What do I mean by "welcoming"?
I see it as the act of engaging someone with the grace and love of Jesus without strings attached. The opposite of welcoming might be to stay at a distance, give them the cold shoulder, or worse, to confront them for their sin before building a relationship.
The top priority for the church when engaging new guests is not to point out their sin but to point them to Christ. A person can only repent if they really know who Jesus is. People don't repent to an institution or a religious system, but to a person—the person—of Jesus.
Let's face it—grace is scandalous. I often need reminded that God extends grace to everyone—evil dictators responsible for genocide, cold-hearted sex traffickers, adulterers, liars, middle-class men who cheat on their taxes, and women who cheat on their husbands, homosexuals, the religiously prideful, and the young child alike. It's the radical otherworldly mercy of God that still has even the most astute Christians scratching their heads.
At any moment’s notice, none of us are that far from the Pharisees when they said, "This man eats with sinners and hangs out with drunkards and prostitutes!" In other words, this guy is taking the whole God thing too far; I'm out.
Grace is messy; there's no way around it.
Jesus often engaged people who were leading sinful lifestyles, but he rarely (save the religious) slammed them about their sin in his initial welcome. Instead of a four-point sermon on the evils of adultery or greed, Jesus often met with them for dinner, chatted with them by pools, told stories in the marketplace, and pointed them to the Truth.
When Jesus spoke with the woman at the well (John 4), he didn't go right to her sin but discussed true worship and living water. Yes, he called her out on her lifestyle (perhaps more to show his divinity than to stir up guilt?), but the conversation was a steady flow of grace and truth, love and mercy, and, yes, acceptance. The end result? A whole village hears the good news.
When Jesus met with Zacchaeus (Luke 19:1-10), he didn't initially call him out for extortion and greed but asked him to go to his house and have a meal—again, pretty scandalous for a Rabbi to sit at the table with a known sinner. The end result? Zach repents and starts passing out money—a lot of money.
In each instance, the Spirit was moving, grace was present, and repentance happened.
These lies are told every day all around our country, and people are believing them.