That's right, a fully open mind is dangerous. There's no need to be open to ALL other ideas, some ideas are stupid...take 90% of my ideas for instance. Another example: if your friend is going to abandon his/her family for some dream of living as a Furry, high on peyote in New Mexico building alters to "Bronies," hopefully you don't "keep an open mind."
In proper moments, a narrow mind can be just as valuable as an open one. Racism, sexism, general forms of "isms," homophobia, sex-craved dolphins, rampant greed, littering, people wearing pinky rings, just a few examples of when we need to snap that open mind shut.
Because the term, "openminded" is too broad, I suggest rebranding the idea of being receptive to new ideas and arguments as "reasonable tolerance." When someone presents you with an idea new to you, simply filter it through the sieve of reasonable tolerance. Those two words puts all ideas through a quick check of, "is it reasonable, and can it be tolerated?" To me it's simple: does the idea negatively affect anyone else, if not, have at it.
On a similar note, if someone wants to believe in the healing power of holistic medicine, fine, good on ya. But if some medicine man tries to sell that medicine or magnet bracelets as being clinically/scientifically proven, that's a lie and doesn't require respectful tolerance because it's predatory.
UFOlogists, while I'm not tolerant of that silly terminology, they're harmless, hence tolerable. But their perpetuation of the xenophobic stereotype of rapey aliens? How dare they categorize aliens as intergalactic anal violators (the worst name for a video game, by the way). Aliens would have figured out human physiology through vivisection long before rectal tomfoolery.
Also, I'd much prefer to be called "reasonable" than "open-minded." Open-minded implies that you can be hornswoggled by people who would use the word "hornswoggled." Reasonable implies that you assess things within cognitive reason.
Robots? Reasonably cool. Whiney British robots with impractical, unbending elbows? I say thee neigh.
So join me in eradicating open-mindedness! Wait, I don't know if that's the message I want to go out on. Eh, it's as good a point as any to end on.