I don't consider open-mindedness to be a particular principle to defend, or even a virtue to value. What is open-mindedness in itself? It is simply lack of knowledge! Or to be more accurate: open-mindedness is being honest about one's lack of knowledge.
The virtue there is not open-mindedness. The virtue is honesty. Honesty with one's self carries with it a disinclination to self-deceive. Open-mindedness by itself is no virtue at all, for if I know one thing, really know it, then I can no longer be open-minded about a proposal that demonstrably, irreconcilably contradicts what I know.
Of course, if what demonstrably, irreconcilably contradicts what I know is observable reality, and not some person's proposition, then what I know must be broken. It must be either discarded or reconceived. It must be reconciled with reality, for knowledge describes reality. Or at the very least: knowledge cannot be irreconcilable with reality.
In practice, people who claim to be "open-minded" can claim it is out of skepticism, but often they're skeptical about the wrong things. We have, in working experience, a model: a description of our universe which is increasingly and powerfully accurate, even increasingly elegant. I call it physics, but I'm not picky about terms. It's the model much of homo sapiens has been scraping towards together since just about before we began wearing eyeglasses. Scraping together, collaboratively, which for us means: competitively, argumentatively. Still we come together. We've been guessing and working out, testing and refining our descriptive models, clashing them against each other, and slowly - seemingly, inexorably - our descriptive models converge.
Today we have quite a coherent and expansive framework, from within which we describe the universe. We predict from it, and get back strong confirmation. Better and best: every single time the model fails, that failure (and the corresponding refinement) advances the model. Every seeming stumble is in fact a leap. And we keep on refining, keep on reconciling our descriptions to reality.
Our goal is to describe the universe. As accurately as we can, to the greatest extent we can. It's pretty great.
But some of the things people have to propose to you...they really don't fit what we know, you know?
For instance. I don't really believe in the reality of telekinesis. Sorry, but there it is. Is telekinesis impossible? Aw heck probably no! How could it be impossible? But let's admit a few things about telekinesis, as long as we're examining the proposition. For one thing: it sure hasn't been very demonstrable. For another, given homo sapiens has had the same brainplan for something like 200,000 years, you'd think a trait so obviously adaptive would be in wider evidence! For a third thing, the theories people advance to explain how telekinesis is supposed to operate don't exactly boost its luster. Ditto, I don't really believe in space aliens visiting Earth. This is not on principle. It's for particular reasons. Or what about the achievability, in practice, of faster-than-light travel through space? I don't really believe in that. The idea of traveling from one point in the universe to another without crossing the intervening space is a different matter, and slightly more plausible. Or what about time travel. I don't believe in it. At least - not to the past. I don't really believe that will prove possible within what physical properties the universe will show itself to have. Within the sum total of all the energy the universe will show itself to have. These are not unknowable areas. There are some pretty damn compelling indications on points like that.
Skepticism is not open-mindedness. Skepticism is simply a refusal to judge in the absence of a compelling cause to do so. Skepticism doesn't oppose holding well-honed and plausible belief or disbelief. Skepticism doesn't oppose leaning towards what you have strong reason to call plausible, implausible, probable or improbable - so long as you have eyes open for its further proof or disproof. Skepticism - to suspend judgment on what's not compelling - doesn't result in "open-mindedness" about what is compelling. It doesn't result in open-mindedness towards what's contradicted by what we know. Given what we don't know, all things are possible! Just as given what we do know, some things aren't plausible.
Skepticism is not a rejection of knowledge. Believing in certain things means disbelieving in other things.