I'm arguing that any person purporting to do Scientific Skepticism must, for the purposes of doing that skepticism, adopt a wholly agnostic position while doing said skepticism. As for the rest of their life, I can't make a judgement on what they believe.

I think we're experiencing a bit of a disconnect, a bit of a 'there is no spoon' moment. It's not that we're talking about agnosticism and gnosticism (gnositicism here meaning the opposite of agnosticism, and not Gnosticism with a capital 'G'). We have to talk about context here -- my argument is not that a person can believe in a God and still be a skeptic, it's that the question itself is irrelevant to scientific skepticism. They're wholly orthogonal positions. Since the existence or lack thereof of a deity is unfalsifiable, it simply doesn't matter what you believe. There is nothing intrinsic about scientific skepticism which precludes you from believing in a god. I might argue that it's unlikely, but unlikely doesn't mean contradictory. I can only make that argument because scientific skeptics tend to also be 'gnostic' atheists -- at least weakly -- but that doesn't mean a theist couldn't also be a scientific skeptic. They would have a hard time being a 'religious' skeptic (for lacking a better term), which would be someone who applies ideas like parsimony and probabilistic reasoning to exclude the notion that God exists.

To put it more plainly, I think you're conflating scientific skepticism (which is, in essence, just the application of the scientific method to questions which the scientific method can help resolve, of which the question of the existence of gods is not one), and 'religious' skepticism (which is, in essence, just the application of parsimony and other circumstantial or pure-logical arguments to challenge the existence of gods, a sort of reverse apologetics, if you will).

Indeed, this extends to any other religious belief you like as well. Nor am I claiming that Religion is above scientific questioning. Religion makes a lot of falsifiable claims (a worldwide flood, for instance; the age of the earth, for another), these we can (and do) investigate and often find wanting. I think that these falsified claims lend circumstantial evidence to the nonexistence of the God purported to cause them, but circumstantial evidences is insufficient to prove that God doesn't exist

I think it's sufficient enough to prove that the Abrahamic God doesn't exist, no?

I think that it's sufficient to prove that a global flood didn't happen (since we would see effects of that in terms of fossil record, etc), and that the Earth is not as old as the Bible claims. That is, it's sufficient to prove that a book written by humans was incorrect about some facts that the authors really didn't have any real chance of getting correct. As far as the existence of a particular God -- it provides some circumstantial evidence that he doesn't exist, but it doesn't prove it conclusively one way or the other. Again, we can posit that God is intervening to make his discovery more difficult (justified perhaps, as I once did, as a test of our faith). The real crux here is that fundamentally Scientific skepticism and Reverse Apologetics/Religious skepticism are orthogonal, neither really effects the other in a purely logical sense.

Now, all this aside, I suspect it's not easy for a Religious person to be a skeptic. I mean, to (mis)quote some old Jewish guy: "It's easier for a rich man to pass through the eye of a needle, then for a religious man to be a scientific skeptic." But in a logical/'someone could consistently hold these two positions simultaneously' sort of way? I don't see any issue with it.