The problem you're going to run into is that there are many different uses of the word irrefutable, depending on one's epistemology. For example, for me, one use of what's irrefutable is what's foundational, i.e., what cannot be coherently or reasonably doubted generally.

Another use of the term might be a proof, i.e., if the premises are true, then the conclusion is irrefutable. Even inductive arguments might be referred to as irrefutable depending on the strength of the premises. But you're going to get people who hold to the idea that their version of the word irrefutable is the only use that counts.

Good luck trying to get unanimity - I've never seen it happen in this forum or any other forum, but don't let that deter you.

Should irrefutable beliefs be valued according to their truth or their utility?
Here, the condition of irrefutable is necessary since otherwise one would clearly value the beliefs according to their truth considering they can be proven to be true or false.

I don't know what these terms mean. Does ignoring the word belief, does "irrefutable" refer to necessary truths? If so, well, so of them ought to be valued, but not fetishized. Every logical or mathematical system has necessary truths. But most necessary truths are trivial or at least uninteresting in most discourses. But for most truths, they are not irrefutable in any sense whatsoever. This is enormously more so for beliefs. Any belief can believe mistaken, none are irrefutable in principle.

belief is only good for the psyke of the person/group of people in question, in a positive way. and beyond that shouldnt be valued at all. a dose of cold logic and absolute truth is what we need.

Irrefutable only means that it cannot be disproved using the data available. — Isaac Shmukler

That which cannot be disproved:

1. It's a fact
2. We don't have enough data to either confirm or deny a proposition.

I guess you mean 2 by ''irrefutable''. Poor choice of words because, usually'' ''irrefutable'' pertains to a sound argument and its true conclusion.

Anyway, given inadequate data to make a decision it is adivsed to suspend judgment until we do have the information that swings our belief. Until such a time one does have the option to choose a side depending on what one prefers.

We could also pick apart an idea and take away what one likes and discard what one doesn't. For instance take religion. We could invest in its moral teachings and reject the superstition.

I think beliefs are quite complex and we may be able to break them down into chunks that are palatable or tasteless.

It seems that my initial formulation is far from being clear. I should try to ask this question in a much simpler way:
What is more important, the knowledge of the truth or well-being?
One of the implications is the answer to the following question: Should one rather believe in what brings one well-being or in what brings one closer to the truth?

What is more important, the knowledge of the truth or well-being? — Isaac Shmukler

Well, that's a value issue isn't it? Which do you value? Well-being or truth? Truth doesn't change for anything. Everyone, the weakest to the most powerful, has to come to terms with this fact.

Well-being comes in all shapes and sizes. What is food for the goose is poison for the gander. This is a, well, truth and what follows is there can be no universal definition of well-being. Of course some have differentiated lesser-happiness (of the flesh) and higher-happiness (of the mind) but this distinction lacks general appeal. We don't see people, when told of it, running to philosophers in search of the proverbial wisdom of sages. This being the case we're unable to use well-being as an anchor for our ships.

Anyway, at the scale of the universe itself, at 13.8 billion years old, which choice you make is inconsequential.

If we are talking about the total Truth, it is the eternity desire(pothos) of the human soul. In greek language the word ''Truth'' is called ''Alithia'' and etymologically means ''what can not be forgotten''.
So i believe that once we had met Truth, and our soul can never forget this <<land>>. And the whole journey of life, only has meaning when we are travelling back to this land, with any cost.
The well-being instead, concerns the earthy desires. It is also a choise, but not for the heroes...

Isn't well-being the application of the knowledge of truth?