I am in occasional contact with religious people, and they don't behave as the "separate magisteria" hypothesis would predict.

For instance, I have heard things along the following lines: "I hope my son gets better." "Well, that's not in your hands, that's in God's hands." All this said quite matter-of-factly.

There is active denial here of something that belongs in the magisterium of physical cause and effect, and active presumption of interference from the supposedly separate magisterium of faith.

Of course most of those people back down from the most radical consequences of these beliefs, they still go see a doctor when the situation warrants - although I understand a significant number do see conflict (or at least interaction) between their faith and medical interventions such as organ transplants or blood transfusions.

This isn't just an epiphenomenal dragon, it's a dragon whose proscriptions and prescriptions impinge on people's material lives.