I think you're missing the point of the account. 

Why would Jesus say, in respect of Zacchaeus:  “For the Son of Man came to seek and to save the lost” (Luke 19:10). We can only understand this to mean that  Zacchaeus was spiritually lost.  It's not a statement about "social exclusion". 

Similarly, so far as being a "son of Abraham", Jesus taught that hereditary descent from Abraham did not qualify one for salvation as the Jews believed. Following Saint Paul, we use the term "Justification". 

Jesus' words to Nicodemus:

"Believe me, no man can enter into the kingdom of God unless birth comes to him from water, and from the Holy Spirit. What is born by natural birth is a thing of nature, what is born by spiritual birth is a thing of spirit."

Zacchaeus was redeemed by His faith in Christ and this manifested itself in a change of heart and behaviour.