It's also got to be a matter of sufficient consequence to be worth the time.
Extraordinary claims require extraordinary evidence, etc.
That is why it is important to support your local crackpot. Much as staid English society always valued their eccentrics. The more ultrarational the person, the more important for that person to spend quality time at the fringes.
There's also the claim that someone is being "close-minded", when they reject an idea they have soundly researched and therefore need not waste any more time on. As Harlan Ellison so eloquently put it: "I'd gotten all the literature I could handle on the subject from a certain Thomas Aquinas" in regards to the god hypothesis. More often than not, "close-minded" is a conversation stopper, designed to deflect from the accuser's very own ignorance and credulity.
Same thing goes for creationism, AGW denial, anti-vaxx, anti-mask, the QAnon cult, trickle-down economics, etc.
It wasn't that long ago that some crackpot tried to convince me that the modern atmosphere had damaged my lungs, so to replace the oxygen I was missing I needed to buy hydrogen peroxide injections. The claim as a whole either needs to have major structural flaws or overturn sizable portions of modern chemistry and physics to have a chance at plausibility, and my biases strongly suggest that instead somebody was trying to skirt legal oversight in order to con me.