One of the central aspects of the ministry of Jesus—one that is continued here—was the fact that He ate with sinners.
This is actually one of the most striking things about the story that the gospel writers tell about Him. Not only did He eat with sinners, those who had been exiled from the ranks of the pious, He often did so in a celebratory way. Not only did He eat with them, but He failed to require them to maintain an appropriate demeanor for sinners in search of forgiveness. Perhaps we could understand His condescension if He agreed to eat with them while they all sat in the dark, nibbled on a cracker, and had a small glass of tepid water. But no, He ate with them in such a way as to earn for Himself a reputation for being a glutton and a drunkard. The slander was indeed a slander, but it began somewhere. It was not manufactured out of whole cloth.
What we may take away from this is that Jesus is not concerned about what your presence here today will do to His reputation. He is not distressed over the possibility that our sin might contaminate Him. It cannot and will not. As far as that is concerned, He just doesn’t care.
In extreme cases, we exclude people from this Table because they are destroying themselves, not because they are destroying the forgiveness that is set before us here. We come because we need to. We partake and are built up and strengthened. We eat and drink, and are identified with Jesus, the one who is willing—by His grace—to be identified with us. And so come.