The Orthodox Chruch maintains that just as Christ's kingdom is not of this world, so must the church be distinct from the state.
From Saint John Chrysostom...
"The decision to receive treatment does not lie with the man who administers the medicine, but actually with the patient. That wonderful man, Paul, knew when this fact when he said to the Corinthians, "Not that we have lordship over your faith, but are helpers to your joy." For Christians above all men are forbidden to correct the stumblings of sinners by force. When secular judges convict wrong-doers under the law, they show their authority is complete and compel men, whether they will or no, to submit to their methods. But in the case we are considering it is necessary to make a man better not by force but by persuasion. We neither have authority granted to us by law to restrain sinners, nor, if it were, should we know how to use it, since God gives the crown to those who are kept from evil, not by force, but by choice.
For this reason a lot of tact is needed, so that the sick may be persuaded of their own accord to submit to the treatment of the priests, and not only that, but be grateful to them for their cure. If a man struggles when he is bound(for he may still choose to), he makes his suffering worse. And if he ignores the words which cut like steel, he adds a second wound through his contempt, and intention to heal becomes the occasion of a more serious disease. For the man does not exist who can by compulsion cure someone else against their will."
And this should make clear a few things.
1. We recognize that spiritual illness is at the root of these issues.
2. We have a therepeutic method for curing these spiritual illnesses.
3. It is not on the healer but the sick to not only to consent to treatment, but follow through with it.
4. We do not heal through compulsion, it has to be in the will of the one being healed.
5. The church is not intended to be a secular authority.
Also worth noting, caeseropapism is recognized as a heresy.
All this said, secular(by this I mean worldy) governments love to exert control over the church!