"Nonsense" doesn't necessarily mean "false"; it means something more like "irrational" or "unjustified".Well, you are free to prove my religious beliefs false, but that is an impossibility. You claim they are "nonsense," but that is not accurate. That would only be the case if they had been shown to be false.
A belief that's logically incoherent could never be shown to be false (since it couldn't be evaluated at all) but still be nonsense. Even if a belief is coherent and internally consistent, Russell's Teapot and Carl Sagan's "invisible dragon in the backyard" illustrate how these sorts of ideas can be nonsense even if there's no evidence against them.