I was asked what I thought about a preacher serving as a chaplain for the Police Department.
My stand is "no" because it leaves the impression that we are in fellowship with the denominational world (II Corinthians 6:14).
I was asked to serve as a Chaplain for a hospital and refused because one of the requirements was that if a terminal patient requested "last rights" I would be required to honor the patient's request.
Much would depend the requirements of the position. Not all are the same. A position that required performing tasks that are not a part of the Christian religion would be wrong, or one that restricted the person from teaching what he knows the Bible to say would equally be wrong. I do know a preacher who serves a chaplain for a prison, but he has no restrictions placed on him regarding teaching and he can decline requests he disagrees with. I suspect such circumstances are rare.