There are several questions here.
First, most people consider their religious beliefs to be a private matter, though that is not true for all cultures. If someone is applying to a school that shares a culture in which god is "worn on the sleeve" then it would be fine, I guess, but in a cross-cultural application it might be unwise for the applicant. Not every place has policies such as yours.
Whether the person will be disruptive or not is unknown and you won't really know unless you have a conversation with them, provided that they are ranked highly enough on proper criteria to merit a close look.
In general, I would consider "disclosing" their religion to be benign and I would even expect to have to make some allowances for some folks so that they can carry out their religious practices. But proselytizing for a particular religion, whatever it is, would likely be disruptive. You might need to have some rules around that, so that people know that they have to keep to the job at hand when working.
As to the title question of letting religion declarations influence your hiring decisions, I would adopt practices such as yours. Your religion is your business, not mine. Other, more relevant, things will influence the hiring decision.