The three components of independent-mindedness work in concert: fastidiousness about truth and resistance to being told what to think leave space in your brain, and curiosity finds new ideas to fill it.
“If your opinions on one subject can be predicted from your opinions on another, you may be in the grip of an ideology. When you truly think for yourself, your conclusions will not be predictable.” – Kevin Kelly
In the most independent-minded people, the desire not to be told what to think is a positive force. It's not mere skepticism, but an active delight in ideas that subvert the conventional wisdom, the more counterintuitive the better.