> h(f) is either 1 or 0

Depending on f. The God-existence function doesn't depend on its input.

You can also say, for example, let f: R->R be defined by f(x) = 1 if I'm a man, and f(x) = 2 if I'm a woman (or non-binary or anything else). Is the derivative of f zero? You don't know what the value is, but you can answer this question with "yes".