I’m not sure if you meant it this way, but your post could imply that a "skeptic" or "objectivist" is the one not having an open mind.
To be clear, that is far from the case. Whether it’s Amir or me or some other like-minded folk, we are open to ANYTHING that is true! That is the whole point of doing rigorous inquiry. We simply ask for good evidence for a claim, especially if it’s an extraordinary claim relative to current generally accepted theory or practice.
Given that countless wild claims are made every day, what other approach could be more reasonable? One should always be "open minded" in the sense of being open to any evidence for some new thing, and ready to overturn any current beliefe we have based on good evidence. But that should always be in the context of how plausible a claim is, and what type of evidence has been provided. We have built bodies of hard-won...and PREDICTIVE knowledge....by being very, very careful this way. If "open mindedness" is not tempered by critical thinking this way, then being "open-minded "may as well be a synonym for a lack of critical thinking about claims - to be vulnerable or gullible.
For instance, if I claim I could sell you a perpetual motion machine, which would solve your energy bill permanently, how "open minded" do you think you should be to the truth of my claim? Wouldn’t your skepticism...and a high demand for evidence, be quite warranted?
It is a mistake to presume skepticism or demands for good evidence equates to close-mindedness.