The phrase “Jesus freak” was originally used to demean/insult Christians involved with the Jesus Movement in the 1960s and 1970s. It was primarily directed towards “Bible thumpers” and those who were especially aggressive in their evangelistic efforts. The core meaning of Jesus freak was a person who was so dedicated to following Jesus that there was nothing else the person could talk about. A Jesus freak is basically a person who is obsessed with Jesus.
While it was originally used as a pejorative, Jesus freak has become accepted and even embraced by many in the Christian community. A “Jesus Freak” song and album by the Christian band DC Talk in 1995 helped popularize the term. This is perhaps similar to the term “Christian,” which seemingly originated as an insult (Acts 11:26), but later became the most widely accepted term for a follower of Jesus Christ. If obsession with Jesus is indeed the core meaning of Jesus freak, then yes, a Jesus freak is precisely what a Christian should strive to be (Matthew 16:24).
In the Jesus Freak song, there is a contrast between how the world views a Jesus freak and what the Bible would declare to be a Jesus freak. First, a man with “Jesus saves” tattooed on his belly is standing on a box in the middle of a city, claiming that he had a dream. That is perhaps how the world thinks of as a Jesus freak. Contrasted with that is the example of John the Baptist. While the world thought he was crazy, he demonstrated the ultimate commitment to Jesus by dying for refusing to be silent: “the king took the head of this Jesus freak” (Matthew 14:10). That should be the definition of a Jesus freak. We should be so radically committed to Jesus that we would rather lay down our lives than deny Him.