The first thing to be said about the nature of reality is that there is nothing natural about it. "Reality" is a human concept. It's not something you stub your toe against. There are different ways in which that concept has been understood (see Absolute Reality, Relative Reality, and Groundless Reality for sketches of three philosophic stances). There are many shades and subtleties to the views that have been put forward over the centuries. We will be ignoring the subtleties and chunking big.
Why bother, though? What's reality to us? We (Gordon and Dawes) emphasize again and again the importance of beliefs in understanding how we humans think, feel, act, and even how we perceive. Beliefs are not stand-alone mental furniture. They cluster together into suites and hang out together in rooms. Sometimes it is as if there is no communicating door between one room and another. Sometimes this leaves us operating out of contradictory beliefs, something we only notice when they are simultaneously stimulated by the same context, creating an "internal conflict."
To push the metaphor to the limit, the rooms of belief-sets are contained in a building, located in a country, on a planet, within a cosmos. When it all starts going cosmic we come to beliefs about things like the meaning of life, the spiritual and religious sets of beliefs, and . . . yes, beliefs about the nature of reality.
In fact, when modeling, we are normally dealing with levels of beliefs that operate within the realm of these "higher" beliefs (or "deeper" beliefs if your metaphoric preference is archeological).
Most of the time we are not thrown into cognitive disarray by any demand that we re-negotiate our beliefs about reality. These tend to be stable, and historically they tended to be even more stable (almost geologic). There weren't too many noisome types going around discombobulating our certainties; and if they did turn up we could always rely on the Spanish Inquisition. Today, though, there is more of a free-market of realities, with a carnival of believers of every stripe and fashion setting out their stalls in the world Mind. So it is now possible to consider ideas about reality as ideas, rather than their simply being the givens of a time and a culture.
This is not to glibly imply that we can simply choose realities at will. Designer realities might sound like fun but there is a mass of personal and cultural connective tissue holding the ones we have in place. This does not mean that nothing can be done. We are not condemned to remain walled in the house of our beliefs. For instance, many spiritual practices exist which are designed to effect such door-opening changes and, as more is learned about the architecture and internal ecology of beliefs, the efficacy of our methods will increase until it becomes apparent how we can choose to accelerate to escape velocity.
At this point, our ambitions are far more modest. The presence of different ideas about reality allows us to consider the influence they have on our experience and their consequences for our behavior, just as we can with regard to our more everyday beliefs. For us, the interest is in how ideas about reality help or hamper our operating effectively in our exploration of experience through modeling.