I think they are both sincere and insincere simultaneously. They are intellectually dishonest, and knowingly use falsehoods to convince themselves and others to believe. Thought stoppers and logical fallacies keep the cognitive dissonance in check enough for them to perform the mental gymnastics needed to keep the plates spinning. Being honest would be very uncomfortable, so they just block out the doubts by any means necessary and blame Satan - they are too invested to do anything else.
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I'd agree with this. I think they sincerely believe in the core doctrines but aren't afraid to use intellectual dishonesty and outright deception to keep the sheeple believing because, in the GB's minds, they're too stupid to attain salvation on their own. It's what lets the GB continue to defend certain teachings and policies they themselves realize are indefensible, illogical, or unbiblical, but would destroy the faith (in the Organization) of too many if they reversed course.
Basically they see their use of "Theocratic Warfare" on their own people as justfiable since it helps keep those people in the Organization.