Religious identity in the U.S. is a tremendously fraught thing, particularly within the public sphere. As a matter of law, courts grant wide deference to the religious beliefs of people and, uh, corporations, generally not assessing them beyond the sincerity with which they are held. It doesn't matter whether there is any factual basis for believing that birth control pills cause abortions; it doesn't matter whether there is any logical connection between providing car service to a same-sex couple and any act by the couple that one might consider sinful; it doesn't matter whether refusing to provide reasonable restroom access to a transgendered employee serves any coherent religious belief. As long as you sincerely believe it, it's a belief that our Constitution and many statutes protect.
Trump draws on this kind of systemic deference for religious beliefs when he takes umbrage at the Pope's criticism. But it's bizarre that he should do so; surely, any politician who cites their religious identity as a credential (as Trump has done) thereby subjects themselves to criticism for failing to merit that identity.
Indeed, there is a strange incoherence at work in Trump's statement, insofar as he presumes that the Pope is being used as a "pawn" in some broader geopolitical plot. Because respect for one's chosen religious identity is, at root, a respect for a person's autonomy on matters of spiritual commitment and morality. But that's all that the Pope is himself exercising, when he weighs on Trump's commitment to Christian principles - he is evaluating Trump's statements and finding them lacking. So by criticizing the Pope, as Trump has done, Trump is really just engaging in exactly the kind of disrespect that he claims the Pope has shown him.