Get rid of terminology

I've just read a very helpful book called 'Pillar & Prophets' by Carl Medearis. Until recently Carl worked in the middle east simply as a follower of Jesus. I heard him speak at New Wine a few years ago and was very impressed in what he said. The book he wrote is about how we as followers of Jesus can talk to and interact with our Muslim friends. I found it a very respectful book and helpful in how to talk with Muslims. His second to last chapter was very helpful. He talks about the question, 'Would Jesus require a Muslim to "convert" to Christianity?' You're initial reaction may be - well, yes! But in Scripture we are never commanded or encouraged to use the word Christian. The Acts reference to 'Christian's' may infer that it was used perjoratively. But Jesus was not a Christian - he was a Palestinian Jew, who was a pain in the side of the religious community. Medearis says that 'his personal mission was not to found a new religion called "Christianity", but rather to...seek and save the lost' (83). He also tels us that Paul says there is neither Jew nor Gentile, etc. There are those who follow Jesus and those who don't. Therefore isn't it possible for someone to follow Jesus but culturally still be a Muslim. Jesus is still one of Islam's biggest prophets. In fact in the past Sufi Muslims lived according to the teachings of Jesus. One of the Muslim monk wrote, 'The person who catches the disease of Christ can never be cured'. He wasn't being nasty in this quote simply stating that once you encounter Jesus there is no turning back. So maybe it is possbile? What do you think?