@Kobuk, Yes, Proof (evidence) is essential to any argument, as shown by Plato's ladder of belief. To further clarify this:
There is a difference between rejection due to close-mindedness (which I am defining as unjustified rejection/disbelief, which is a form of the first rung, unjustified belief) and rejection due to epistemically aware (which I am defining as justified rejection/disbelief, which is a derivative as well, but of the second rung, justified belief) reasons.
If I said, 2+2=10 (and NOT in base 4), you would reject it, because it is disprovable. This un-knowledge (unworthy of even the title of 'belief', though it could be, if you were really deluded/bad at math) can be rejected out of epeistemic awareness rather than close-mindedness.
Now, if I said, God is an alien made of meatsauce and ramen noodles* who despises pasta (and pastafanaians and their false pasta/meatball god) who is part of a government/aztec/alien conspiracy to blow up earth but resulted only in destroying the twin towers on 9/11, and gave no other reason than, "I got it in a holy vision while I was sleeping after eating a 10 cheeze pizza with too many anchovies", you would be right to reject this as being a load of nonsense without doing any real counter-arguing, because I never provided any real proof, and I was just spouting Unjustified Belief (as defined by Plato, this is nothing but dogma with no substantiation). Now if I had some sort of evidence to back this up, making it a Justified Belief (NOT a Justified TRUE Belief, just a Justified Belief), then you could still reject it with a VALID counter-argument, but not doing so could be defined as doing it out of close-mindedness.
It's all about justification. If you cannot/do not** justify it, don't be surprised if people outright reject it, and on the other hand, if someone justifies their belief, you need to provide some sort of justification for your belief.
I'm not saying justification = truth and unjustified = untrue. I'm merely defining the line between rejection out of close-mindedness and rejection out of rational justification.
*Ramen noodles are asian, but I don't know if I spelled that right.
**Some things may not need explicitly mentioned justification however, such as basic arithmetic, which assumes the other already knows of the justifications for this, in other words, basic math skills.