It seems to me there a two major takeaways, one for conservatives and one for progressives.
For the conservatives, we are to show up in any place and with anyone without a word of judgment or condemnation. This is exactly what attracts progressives to Jesus, and they are exactly right in calling out conservatives for their failures on this point. Simply put, culture warring Christians are not Christians. As we've seen in this series, Jesus was hardest on those who, through a religious/moral caste system, marginalized others. Jesus' calls for reconciliation were not directed at the sinners, but toward the righteous.
For the progressives, Jesus' friendship with sinners had an evangelistic purpose. Jesus was seeking the lost. He was healing the sick. True, Jesus did not hector, lecture, or wag a finger, but he desired transformation and change. And if I'm right about the apostle Paul, this transformation had to do with an encounter with Jesus himself. If conservatives fail due to culture-warring, progressives fail because they are poor evangelists.
One attempt to say all this in a simple way, which I think gets at what I'm trying to describe here, is the refrain that belonging precedes believing and becoming. When I look at Jesus' practice of table fellowship that is what I see. Jesus' embrace shared the good news that the lost sheep of Israel belonged. They, too, were children of Abraham. They were family. And that belonging enabled transformation. This, I think, gets us close to the gospel stories. Belonging first, but with an eye toward becoming. As I've described it in this series, the grace Jesus embodied was both prevenient and transformative. Following Paul, Christ died for us while we were sinners. We're already saved. We're already in. And that prior belonging changes our lives.
To be sure, this is a delicate business that often goes awry in both conservative and progressive spaces. But in my opinion, this path gets us closest to what Jesus was doing in the gospels when he welcomed sinners.