OK--let's go with this analogy. There's a lot that can't be on the other side of the door: square circles, frozen fire, tall abysses, triangles whose interior angles sum to more than 360 degrees, immortal fudgsicles, colorless green ideas sleeping furiously, and on and on. Contradictions don't exist--neither on this side of the door nor on the other side.
And the analogy is far too charitable to the true believer and dedicated agnostic. The true believer is willing to maintain that contradictions exist; the dedicated agnostic that it is impossilbe to know whether contradicitons exist. So, to make the analogy exact, the true believer and agnostic would maintain that (for example) there is a square circles on the other side of the door, but that whenever you open it, the square circle hides from you!
There is a simple answer for this kind of unfalsifiable claim: there is no difference between a negative and unfalsifiable hypothesis. There is no difference between "there is not a green dragon in my garage" and "there is a green dragon in my garage but it's never there when you look for it." God is simply a green dragon in someone's garage that always happens to be hiding whenevery you look for it--meaning, it's basically not there.