The god nutters. People who believe literally in angels or the literal word of the bible in general.
People who believe in the "Law of Attraction" or "The Secret". Open yourself up to the possibilities of the universe and I'll stuff you full of something.
People who believe in the healing powers of crystals or magnets. (or whatever new loony tunes thing they believe in this week; it changes pretty fast; ions? silver?)
People who buy the ShamWow.
Onto that list goes people who believe that "too much regulation" somehow caused the massive corporate malfeasance, or that with less regulation companies will behave better (!?). People who believe that some homos in their town will somehow turn everyone gay. People who believe that the Ay-rabs are all out to get us.
There's a ton of people that you just cannot talk to about the main topics in their lives. God nuts are a prime example, but so are the crazy "America is Great" crowd. Your only possible responses are "uh yeah, great" (with eye roll) or "you are nuts and here's why" (leading to huge argument), there is just no middle ground of reasonable conversation with them because they paint themselves into a corner of ridiculousness that can only be either ignored or attacked.
I was thinking about this because it comes up in less extreme cases as well. For example when programmers are like "our method is totally awesome" and you try to gently point out some inconsistencies and they're just like "oh no, it's awesome, we used it in X product and it all works out fine". They've painted themselves into a corner of oblivious ridiculousness where your only options for response are "umm, okay" (with eye roll) or "no, look dumbass, your algorithm is N-squared and there's no way that's okay when O(N) solutions for this problem are extremely well known; there were 20 papers published before you did your work all of which had better solutions" (or whatever).