Conspiracy theorist (nut) is just a label for people that can think critically, or for themselves.
It's actually the exact opposite.
A "conspiracy nut" is usually both poor at critical thinking but also oblivious to that fact, this is why they choose to believe conspiracies over the significantly more plausible "official" stories in the first place, they selectively choose facts/theories to fit what they want to believe and dismiss any evidence that contradicts their belief, rather than believe what the facts/evidence imply.
There are many many examples of the practice but here's a couple of the most common ones:
Chemtrails nuts wanting to believe the theory so much that they can completely ignore the fact that even if you remove the cargo, passengers and fuel from a plane you couldn't physically fit that many chemicals on a plane and even if you used magic to do it it would then be too heavy to take off, nevermind cruise at it's normal altitude/speed.
9/11 nuts actually being able to watch a video of the towers falling at sub-freefall speeds, with their own eyes, and yet believe they're freefalling simply because their narrator and desire tell them so.
Generic nuts ragging on the BBC for being super biased simply because it's generally balanced coverage doesn't mirror their own personal bias (the fact both the right and left wing make this complaint should make it obvious to any of them capable of critical thinking but no).