"All God's children are not beautiful. Most of God's children are, in fact, barely presentable." Fran Lebowitz
How is that for a quote? The problem has been that church makes people think they are beautiful, and so they have often rejected the barely presentable. They have acted as though they were never unpresentable.
The reality is that Jesus went to those who were barely presentable. He went to those who needed a physician. I think there are very few churches on the planet that would ever say they don't accept people. They feel themselves open to the hurting and the broken. But, for some reason, the people on the outside see them as unwelcoming.
I think this issue, like evangelism, is one of those things that most churches accept in theory but not in practice. Just look at the reaction of most churches when a tatooed, pierced, multi-color haired person walks into their service. They may get a "friendly" welcome, but we all know what happens behind their back. That is one of the exciting things happening with many new churches and church plants.
Steve Taylor did a song called "Jesus is for losers," and I think that is right. Jesus came for the broken, the hurting, the lost, and those who are willing to say, "I am fed up with what life is giving me because it is not working! What do you have Jesus?"