Another thing I'll add after having spent a few years in a religious cult:

It's all about the axioms. If you tweak the axioms you can use impeccable logic to build a completely incorrect framework that will appeal to otherwise intelligent(and often highly intelligent) people.

Also, people are always less rational than they are able to admit. The force of things like social connection can very easily warp the reasoning capabilities of the most devout rationalist(although they'll likely never admit that).