Should I finish staining my half-stained deck with rain coming?
We're thinking of staining our four year old deck soon, and my only credentials are that we've thought about this scenario.

If I were you, I would go ahead and apply the first coat to the remainder of your deck, basically ensuring that all surfaces are evenly covered. If it does rain and screw up everything, at least the screw-up will be consistent.

I realize humidity will be an issue, but are you planning on covering the deck while it's raining? Cover it when raining, let it dry up when sunny.