In Judaism yes; in Christianity not so much, as Christianity claims its rules (and its salvation) are for everyone, not just for one people. Are Jews allowed to hire non-Jews to do things that violate the laws of Noah, which are claimed to be universal? I'd be surprised ...
er, the stereotype of Jews as moneylenders came about partly because of the Christian prohibition against moneylending. It's not a direct case of hiring someone to do a forbidden thing but it's close, and I think the precedent it sets would allow for the existence of a center of theological debunkment.
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.)