No different than the believers who "know" the reality must conform to the way they believe it is.
But if there is structure and order in the universe (and we perceive that there is), then there must be something universally "true" at the foundation of the order we perceive. Otherwise the world would be one way this instant, and something entirely different at the next instant. In short, the universe would be fundamentally chaotic. But if so, then why are things persistently the way they are, and not some other way?
Such a view requires denial of the universal order which we do perceive. Such a refusal to apperceive the obvious constitutes an "opinion" that rests on nothing but a refusal to recognize that truthful human knowledge is the product of engaging the real world by observation and experience. This is to acknowledge that there is a "givenness" to the universal system of which we are parts and participants. That givenness entails that the phenomenal universe (which we perceive to be ordered) and the human mind (which also possesses order by virtue of its capacity for logic and reasoning) can be brought into correspondence. This is the basis of all truthful knowledge. This is the basis of science.
Case in point: There are many fans of "eternal universe," "steady-state" or "boom-and-bust" cosmological models. These opinions are increasingly being undercut by physical observations of, e.g., the cosmic microwave background radiation, and the cosmic expansion, which point to a real beginning of space and time. Despite the accumulating evidence, many still cling to their preferred opinion that the universe is eternal, and/or steady-state, and/or boom-and-bust.
In effect, the holders of such views are attempting to make their own preferences the measure of what the universe is. All such views seem motivated by a deep distaste for, and desire to avoid the "origin problem," i.e., a universal beginning of space and time in a unique cosmic event. In other words, a creation event. They cling to their preferred opinion, despite the piling up of evidence that refutes it.
What is the value of an opinion (or as you put it, a "belief") that can be falsified on the basis of evidence, logic, and reason?
I'll probably have more to say about this shortly. But this will have to do for now.
Thank you so much for writing, dear kosta!