I hate it when people assert that they are open-minded, because they almost never are. And anyway, I think "open-mindedness" can't be regarded as a static quality that people possess in a more or lesser degree but a mental practice - sometimes people think in a mind-opening way, and often they keep their mind closed.
It's been my experience that the more vocal someone is about their "open-mindedness", the more closed-minded they actually are. I first noticed this with the hippies in college. They all preached open-mindedness but only listened to a handful of bands; The Grateful Dead, Phish, Rusted Root etc. while being very closed off to other genres of music. It made me leery of two things 1. Anyone claiming open-mindedness and 2. Drum circles
Brings up an interesting point about supposed open-mindedness. In the case of hippies and redditors they are only considered open-minded relative to the general population. But internally they show the same closed off opinions as anybody else just with different biases.