Yes, it is true that the people who most speak about questioning authorities, independent thinking and open-mindedness are conspiracy theorists and other crackpots.

On the other hand, I suspect the reason for that is partly that we are taught that it is good to think critically, while nobody actually explains how to think critically. For example, "question authority!" is a pretty poor advice when not explained in greater detail, and this is how we usually get it. No wonder a lot of people interpret it as an endorsement for indiscriminate questioning, which may be translated as "believe whatever you want".

I suspect that if biases and rational thinking were taught in schools, probably less people would describe themselves as "rational", but a lot of people would be far better thinkers than they are today.