They should be able to deal with strong emotions. We Christians tend to forget that God Himself gets angry and that our Lord was so angry at the greed and corruption around the first century Temple in Jerusalem that He overturned the tables of the money changers. We are also told to hate evil. The problem of suffering is hard enough for any minister to explain to someone in pain or loss. A minister's first exposure to switching between personalities ideally should take place with the individual's therapist present so that the minister has the opportunity to become comfortable with observing and interacting with alternate personalities.
Ministers can learn a lot from watching how a therapist talks to the alters.
By all means the minister and therapist should have signed permission to speak with each other about their work with the individual with D.I.D. and the minister should be able to contact the therapist any time. One excellent observation they made follows. When patients are suspicious of secular therapists, challenges to religiously based resistance require clergy involvement. By allowing clergy to address the resistance, the therapist escapes being viewed as the secular attacker of faith. This consists of the therapist and clergy meeting together with the patient to confront persistent religious distortions that block progress.