I don’t know the history of the song but Depeche Mode’s Personal Jesus sounds like a parody of TV evangelism. To me, it also describes the basic flaw of so much of contemporary Christianity.
As I pointed out in a previous post, there is no being a Christian without being a “churchian”. We treat the church like a byproduct of Jesus’ work, but it isn’t. The most reasonable interpretation of Jesus was that he was a man who looked at the religious and political situation of first century Israel, saw it was headed for collapse, and decided to start a new community. The church is Jesus’ artifact, his life’s work. So while yes, you can have a personal relationship with the Lord, he is not your personal Jesus.
The song describes a faith oriented towards feeling better, expunging guilt, having an imaginary friend. It is what some sociologists call Therapeutic Deism. It has no objective pole, no horizon beyond the subjective and personal. In short, it has no church.
This sort of solipsistic / autistic Christianity has its manifestations on what we might call the Christian Left (Jesus is OK with me leaving my spouse for my lover because it feels good) and on the Christian Right (Jesus tells me through Bible that my heresy which has been condemned by the church for 1800 years is actually correct). The authors of the New Testament would not recognize it.