I'm reminded of the guys who went out to search for the remains of Noah's ark. At least some of the people going out and looking for the Ark really expected to find something and change the world - these are the sort of people who would help empirically test religion. Some of the others were frauds - they would be against a test of religion if they weren't the testers. But what of the people who not only didn't search for the Ark, but predicted that it wouldn't turn anything up, and yet still believe in its literal truth? These are the sort of people who don't want to look too hard at their beliefs. They just want to comfortably believe what they like, and would not support uncomfortable prodding.
Lots of charlatans spend lots of money advertising diets and health products that don't work. We have a National Institutes of Health that, among other things, funds studies that make more-objective pronouncements on diet and health.
Argue pro or con: It would be a good investment (payback would exceed opportunity cost) for the US government to create a National Institute of Theology, that would fund research into theological questions. For instance:
Everyone, religious and atheist, should be motivated to want the answers to these questions to become widely known.
(Yes, I know this would be politically impractical. Pointing that out is not interesting. What is interesting, is whether such a NIT would be beneficial, supposing it could be made.)