I suspect among the entire demographic there are both, and some who are simply too emotionally invested in their belief to recognise how closed minded they are.
What baffles me is not that some are geniuses in their professional life, but that they produce the same irrational arguments and anecdotal claims when asked to support their beliefs.
Lets try a simple example of a basic error in reasoning, and I have had this conversation:
Theists: “How do you know a god is not possible?”
Me: “I don’t know this, I have never claimed this?”
Theists: “Aha, so you admit a deity is possible?”
Me: “Sigh, which bit of I don’t know slipped past you there?”
Theist: “Ok fair enough, but you must admit it might be possible?”
Me: “No, because…wait for it, I don’t know whether it is possible or not.”
Theists: You’re just being closed minded."
Me: “I don’t think closed minded means what you think it means?”
Theist: Whatever, you atheists just won’t accept the evidence."
Me: “What evidence?”
Anyway you get the gist, and I never tire of saying this, well sometimes it become irksome, but 1) not knowing whether something is true - is not evidence it might be true, or that it is even possible. 2) Leaping from not knowing something to any unevidenced assumption about it, is not being open minded. 3) I tend to withhold belief from claims if I don’t whether they are true, as this infers the claim can’t be supported by sufficient objective evidence.
As a footnote when a religious apologist, or anyone for that matter, claims to know something is true, if they can’t share this knowledge then they don’t possess it.
1.Facts, information, and skills acquired through experience or education; the theoretical or practical understanding of a subject.
Note that knowing a subject, and knowing it contains something that is true are not the same, see the oft used appeal to authority fallacy “Most biblical scholars believe.”
Oh and while I am on a roll / rant, lets expose the claim that “you believe Alexander the Great is real, so why don’t you believe Jesus was”? This is a false equivalence as I don’t believe Alexander the Great (if he existed) was anything but human, and that is precisely how I feel about Jesus. I am also dubious that there is more historical evidence for Jesus than Alexander the Great, because it demonstrably bullshit, for example we have coins with Alexander the Great’s likeness on, so we even have some idea what he looked like. Paradoxically when someone says they saw Jesus’s face in a sliced tomato, I always wonder what they’re comparing it too?