There is one thing the synoptic gospels agree on — Jesus spent a lot of time eating with “undesirables”, so much so that the religious leaders of the day were upset that He spent so much time with sinners. (For the record, we are all sinners.) The fact that He did it so often means it was intentional and we need to know why. Jose Tolentino Mendonca is helpful here:

By accepting to eat with sinners, Jesus was violating the powerful system of purity. But the truth is that Jesus' gesture is not merely one of rupture, but the affirmation of a new experience of God. In the line of the universalist interpretation of the messianic banquet foretold for the future by the prophets, Jesus was claiming for his “today” a religious way of life that went beyond the bounds of legality by bringing those who had been excluded back to friendship with God. (Jose Tolentino Mendonca, No Journey Will Be Too Long [New York, NY: Paulist Press,2012], 73.)

In Jesus’s time as in many societies today, an invitation to a meal was an invitation to friendship. At some point Jesus would call people to repentance, to turn away from a life that is lived as though God doesn’t exist to turn back to the loving Lordship of God. But there is no mistaking the gesture of being invited to a meal. God was offering His friendship. In other words, God wasn’t just offering a transaction — accept me, escape hell, and go to heaven — He was offering a relationship.

He (Jesus) does not look at sinners in the abstract, or in an attitude of making excuses, but seeing each one integrated in the concrete historic situations that serve as a point of departure for a true friendship, which is always a transforming experience. (Mendonca, 73.)

I guess if all God had in mind was a transaction, He could have just offered it from heaven. He needn’t have come Himself.
Again, Mendonca is helpful in pointing out the significance of Jesus’s table fellowship with “undesirables”.

For the Pharisees and scribes, Jesus went much too far in his table fellowship by sitting down at the same table with sinners, since such table fellowship established a link between them. They did not want to see the extent to which Jesus’ friendship provided the opportunity for a radical conversion that was inaugurating the time of the Kingdom of God in those particular lives. It is certain that the experiences of mercy and of God’s forgiveness are not strictly speaking, a novelty relative to the earlier biblical tradition. But this insistence, prefigured in friendship, of a gift of unconditional and immediate divine mercy (it is not the sinners who are converted in order to obtain mercy; the sinners receive mercy and so are converted!), is so unusual that it appears to be scandalous. (Mendonca, 74.)

There are many reasons why it is hard to preach the gospel today. In fact, I don’t think it has ever been easy to preach the gospel. But the Great Commission remains a key commandment of the Lord’s (Matthew 28:18–20). In an increasingly lonely world, we can’t just take Jesus’s command seriously. We must also take His method seriously. And He is not just offering a deal. He offers Himself. As people who have supped at His table and have been transformed by His mercy, we invite others to His table by inviting them to ours.