If you are looking for a common characteristic, the most common might be the ability to question what we are told to dare not question.
See, this is the attitude among conspiracy theorists that I find a bit frustrating. (and I promise I'm not trying to pick on you in particular here)
They act as if it's everyone else that's closed minded and "sheep" if they're not willing to entertain conspiracy theories.
There's a key distinction to be made when it comes to determining closed-mindedness. ...and that is, has the assertion already been studied and debunked numerous times by well-qualified research?
For instance, if a doctor or researcher claimed they had developed a new compound that could cure HIV...
If they provided detailed thorough notes on their research, showed the usage of substances that have established antiretroviral properties, and showed some promise during initial testing in a lab environment... If someone immediately dismissed it for the concept was fully tested, that would be closed-mindedness.
However, if an alternative practitioner (with a history of defrauding customers) made a similar claim, but showed no peer reviewed research, and the proposed treatment was wearing magnet patches (claiming it manipulates the iron in your blood, a debunked principle), and consuming a homeopathic preparation (also debunked) of cherry stem extract and arsenic... Immediate dismissal of that idea isn't closed-minded, it's called using basic logic and common sense.
Immediate dismissal of ideas, and determining whether or not said dismissal constitutes closed mindedness, ultimately depends on the merit of the idea.
For instance A) 'Established scientist develops a new fuel cell that he claims is more efficient than current ones', and B) 'Guy on
Natural Medicine Blog says gargling with mustard water cures cancer' are not ideas/concepts that merit equal consideration in order to make one "open-minded"