Rational thinking is a method of processing facts and assumptions. It can be applied to as little or as many facts as one chooses, and as little or as many assumptions as one chooses. So my examples are certainly examples of rational thinking, albeit with a highly reduced set of assumptions and facts chosen to illustrate the point.

Also, B clearly was a lying windbag too. But that was a suggestive data point, not proof.

It most certainly was a proof:
Assumption: B lies.
Fact: B claims H has nukes
Conclusion: B's claim is not true

You cannot claim that the above isn't rational just because you disagree with the limited scope of the universe of discourse in that example. In your own example, the fundamental possibility of divergence remains:

I didn't believe that H had nukes because a workable WMD program is almost crippingly expensive, even for a functional economy, and after GW I Country I certainly didn't have a functional economy.

A rational person can still disagree with you by disagreeing with some of your unstated underlying assumptions, such as e.g. that H had actually had them built fully rather than only partially say, or that he had them smuggled in, or that a workable program is much less expensive than you believe etc.

Unless you happen to be a WMD scientist, all of your assumptions about H and his country were derived from interpreting media reports available to you, together with the meta-assumption that these reports were not all outright lies and misinformation. A conspiracy theorist could read the same media as you, but because he assumes that they are outright lies, he will end up with a rather different interpretation, yet both of you would be exposed to the exact same facts in writng and both of you would be rational, you only differ in a highly influential assumption.

Religious people and paranoid exploding-earth nutters are swayed almost entirely by their emotions and don't do logic at all. 'I feel it' isn't much of an explanation for anything, which is why you can't argue with it rationally. Meanwhile the paranoid nutters enjoy drama and fear for the sake of it.

I'm not saying that all religious people and conspiracy people *are* behaving rationally, I'm saying that even if they were, it would be insufficient to overcome the boundaries of their world view. Thus it is meaningless to blame their differing views on a failure to think rationally or to process facts.

Two people who are entirely rational but whose prior assumptions differ can both interpret common facts logically, and end up disagreeing even more afterwards.

--
$E(X_t|F_s) = X_s,\quad t > s$