It's generally acknowledged that open-mindedness is a virtue. But there is some confusion as to what it actually involves. Too often, people confuse open-mindedness with indecisiveness. They think that open-mindedness requires that one abstains from drawing conclusions; hence the absurd tendency to claim that agnosticism is the most reasonable religious stance, solely on the basis that God's existence can be neither proved nor disproved with absolute certainty. I've previously explained why such a stance is misguided. We have ample reason to disbelieve in gods and faeries, and the virtue of "open-mindedness", properly understood, shouldn't ask us to pretend otherwise.
The trait of open-mindedness is best understood as a disposition, rather than an occurrent state of mind. It's not about what beliefs you actually have, but how open you are to revising them in appropriate circumstances. It requires the true humility of self-acknowledged fallibility. It requires that our minds be open to new evidence. But this is something very different from suggesting that we should be equally accepting of nonsense as we are of sense. That's not open-mindedness; it's gullibility, or perhaps stupidity.
The virtuously open mind is not wide open, indiscriminately accepting of any and all viewpoints. Rationality must remain as a filter. We should be open to accepting good reasons of which we are currently unaware. But this doesn't require us to take recognizably bad reasons seriously. If we judge that the weight of reasons favours P over not-P, then we should (tentatively) believe that P. Open-mindedness means that we will acknowledge the possibility that new evidence could in future lead us to change our mind. But it doesn't preclude our drawing reasonable conclusions in the present.