That sentence or its variations is a favorite of proselytizing theists. In essence they are saying unless you believe like they do clearly you must be close-minded. Or more succinctly, open your mind and let your brain fall out.
1. having or showing a mind receptive to new ideas or arguments.
2. unprejudiced; unbigoted; impartial.
Given the definition, it is irrational for theists to posit that unless one accepts the religionist’s belief once it has been fully explored, evaluated and discounted as irrational, that one is not open-minded. Most of us have been exposed to and/or explored religious supernaturalism; those of us who see no logical basis for it, no visible means of support, no evidence of its efficacy reject it. That’s not being close-minded, it's being discerning.
It would be akin to telling someone who tasted and disliked an exotic dish that they were “close minded” for not liking it like you do. They would only be close minded had they declared it not to their liking having not first sampled the dish.
911 and the Obama hating "Birther" conspiracy theorists continue to retain their hold on delusion and conspiratorial nonsense in the face of a preponderance of verifiable and testable evidence to the contrary. No amount of evidence that discredits their delusion will ever change their mind. That is close-minded absolutism.
Meanwhile those of us who have heard their conspiracy rants, read and evaluated their “proofs” and rejected them as tainted wishful (hateful) thinking; and examined the independent overwhelming genuine evidence for no conspiracy and accepted it unless and until objective evidence of conspiracy overwhelms the evidence of no conspiracy, we are accused by these nuts of lacking an open-mind.
One would lack an open-mind, if they rejected the conspiracy theories or religious precepts out of hand without having ever examined and explored them. I have examined them. I have explored them. In the case of religion I have done so in its many different flavors and varied perspectives. And using my powers of reason and ability to weigh evidence, I reject it as superstitious nonsense unless and until objective evidence of the divine is presented that will change my mind. What could be more open-minded than that?
Creationists / religious fanatics reject science having never actually read a genuine scientific source document. I’ll speculate that not one in twenty-five thousand Creationists have actually read Darwin’s On the Origin of Species, or Dawkins’ Greatest Show on Earth, yet reject Evolution and natural selection as fallacy. That is prejudiced, that is partisan, and that is non-receptivity to the input of new ideas or argument. That is close-minded. It exists because just to investigate (never mind accept) the voluminous scientifically corroborated evidence for Old Earth and Evolution from a vast array of disciplines would undermine the efficacy of their belief. It’s a denial reflex. It's the hallmark of the absolutist.
When you hear an Evangelical fundie pull the old “…if you were more open minded…” ploy, tell them which Biblical verse is among the most incredible and unbelievable to you and why. Then ask them which of Darwin’s specific detailed observations on the island variants of the Galapagos tortoise in support of natural selection is least credible to them and why. The open-minded will always vanquish the mindless absolutist.