A pedophile, Christian or not, should be willing to be identified as a sexual deviant in the body if their reasons for attending a church are pure. The priority of the leadership should be the protection of innocence in the church. Not the protection of one individual's right to hide their sexual deviant behaviors. I do not see hiding someone's dangerous behaviors from vulnerable people as loving or Christ-like.
If the church wants to get real about the epidemic of childhood sexual abuse, then the body of believers and their leadership need to start talking about it more openly. Where is the right place for a sexual predator to fellowship? How should their identity be accessible? The church also needs to be realistic about the long-term monitoring that a sexual predator needs.
A pedophile in particular should not be around children. Pedophiles should seek out Christian fellowship in adult-only groups. Even in an adult-only group, the pedophile should be transparent about their deviant behavior so each person can choose if they want to fellowship with the individual.
Separation from children is a burden the sexual predator must bear for life.