Answer by Ernie Jones:
Of course the existence of deities can be proven or disproven.
Anything that's real, anything that exists and is not totally walled off from us in another universe or something — in which case we can have no notion of it whatsoever and therefore no name for it or conversations about it — must provide some sort of evidence of its existence.
And anything that leaves evidence of its existence is subject to rational inquiry.
Now that the scientific worldview has replaced the mythic worldview for intelligent, rational, educated people, it's possible for us to examine claims about deities. They all fail.
In fact, at this point, successfully proposing the existence of a deity is impossible. If you say that your deity is exactly equal to the laws of physics and no more, then you're no longer describing a deity. If you say that it's not, that it is both supernatural and "real", then you're contradicted by the evidence.
It's a no-win for the gods, I'm afraid.