For reasons unimportant to the question all divine/infernal beings ceased contact with humanity in the dark ages. For reasons equally obscure they are now back and busier than ever. Law enforcement, mental health professionals, the legal system, and our nation's corrections system are struggling to deal with the influx of supernatural related crimes. The police utilize a field test to differentiate between the demonically possessed and mentally ill. The suspect is held in a position where they cannot see what the police are doing and exposed to various holy icons from various religions alongside control sample items in order to elicit a supernatural response. This is used to determine the presence of a supernatural entity as if they react to an object that a non-possessed person could not see they are possessed. This test is used to determine the entity's culture of origin, and the severity of the manifestation and helps to target the response (For Example, You don't bring a catholic priest to exorcise a djinn, and you don't bring a native American shaman to cast out a judeo-christian demon.) Tactical Squads of commando-priests, sometimes with an angel or other divine entity on staff are used similar to swat, they are called in to perform field exorcisms upon determining the presence of a malign entity. Keep in mind that all cultures demons, angels, and assorted spiritual entities are now real and said priesthood is not necessarily catholic or even christian. There is a need for a multitude of religious and spiritual holy men to serve as commando-priests. A squad will typically represent several religions.
A coalition of demon and infernal entity civil rights advocates begin pushing for demons to be granted person-hood and civil rights after a demon that is possessing a man claims that an exorcism would constitute cruel and unusual punishment. Up until this point extremist groups have been using demonically possessed as a sort of supernatural suicide bombers in a series of religiously motivated attacks. The controversy surrounding this case is similar to that of the confirmed terrorists being tortured clandestinely in Guantanamo bay.
A movement to abolish the practice of using angel-squads and commando priests to conduct field exorcisms is started. Their chief argument is that government sanctioned religious personnel are a violation of the United States Separation of church and state. The Demon Rights Advocacy Group (DRAG) is essentially a new tactic by the infernal beings to gain power and cause more havoc, but their (non radical) human members are within their rights under the first amendment.
Would a militarized priesthood or the utilization of state sanctioned divine beings operating as law enforcement violate the United State's separation between church and state? Assume they only have jurisdiction over events involving infernal beings.
The debate over the separation of church and state has a long history in the U.S., where the story is set. Please include references in your answers.