It seems to me that some people take the notion "Never accept anything uncritically!" (or equivalently, "There are no certainties in science!") too far.

The core tenets of logic as set out by Mill, at least, must be accepted uncritically and never doubted, or the whole conversation in which they are doubted disintegrates into fallacy and nonsense, and thus becomes useless (except to a dishonest speaker who might use it to manipulate irrational people). There are other beliefs which are similarly necessary (for instance, mathematics) if the discussion extends to topics where they apply.