Confirmable but unfalsifiable?

In my encounters on the internet, I've found that people have all sorts of views on the relationship between science and religion. Here's one that I feel is just plain contradictory, as if someone had taken two very common views and stitched them together into a paradoxical Frankenstein monster.

View 1: God is unfalsifiable. Therefore, you can't prove that He doesn't exist. Those atheists are so irrationally dogmatic!

View 2: Religious experiences probably attest to some unknown. We call that unknown God.

Conclusion: It's a double-whammy! I can show that God most likely exists, and you can't disprove him. I win. Er... I mean, God wins.

See the contradiction? If you didn't see it, I'll eventually get to it.

There is a common theme in the reaction to the atheist movement. "Those atheists seem to have the same conception of God as do the fundamentalists! They probably think he's a bearded old guy in the sky in white robes. That's nothing at all like my religion. God is not something we need proof for." Sometimes, this complaint sounds very silly, as if people were saying, "Why are you giving all those B-movies bad reviews? You should be reviewing my movie." But I'll concede that there is some basis to the complaint. When it comes to fundamentalists, point by point refutations are common. When it comes to "liberal" Christianity, it seems like dismissiveness is the norm. I personally try to avoid this. As an atheist, I have little right to define what kind of God other people believe in. For all I care, you could define God as the ceaseless creativity of the natural universe. I can't really refute that kind of God. The best I can do is criticize your communication skills, and then be on the look out for the equivocation fallacy.

I want to focus on one particular part of the complaint. Most people will say that God doesn't need proof. Apologetics is not very important for them. God is not a scientific matter. God is unfalsifiable. Can they explain why they believe this? But never mind the reasons. The theist gets to define God, and I'll go with that definition at least for a while. Let us presume that we have all agreed that God is unfalsifiable, and therefore unscientific. Let us also ignore, for the moment, my misgivings about the definitions of science, the philosophy of falsification, and unprovable gods. So we agree that "God exists" is an unfalsifiable claim. This implies that "God does not exist" is also an unfalsifiable claim. For how can a claim be scientific if its negation is not?

So if God is unfalsifiable, that means it is also impossible to confirm God's existence with scientific evidence. You cannot refer to religious experiences as a confirmation of God's involvement with humans. You cannot refer to Big Bang Theory as a confirmation of God's creation. You cannot refer to quantum mechanics as a confirmation of God-given free will. If any of these scientific discoveries give you the slightest bit of "It's just like Christianity told us all along!" feeling, that means your god is confirmable, and therefore falsifiable.

So we're back to the top. The two views I presented, each of which I commonly encounter on the internet, are incompatible. One says God is unfalsifiable. The other says God is confirmable by religious experiences. But you have to pick one: confirmable or unfalsifiable. Otherwise, you've got a contradiction on your hands. And this is before I've even started talking about the argument from religious experience. Is it any wonder that atheists tend to be dismissive when people don't take seriously the meaning of "unfalsifiable"?