Any input that our brain conceptualises is an invariant representation. That not only includes representations of physical objects, but of thoughts, ideas, and beliefs.
But beliefs are opinions about
reality, in other words opinions about those representations. They would be retained as invariant representations, but that doesn't mean all invariant representations are beliefs.
Unless you define perception as belief or opinion. E.g., if you would look at a person and think, "I believe there's a person there," rather than, "There's a person there," then you could consider invariant representations to be beliefs. But most people don't think that way, and I don't believe our brains work that way either. I.e., perception is not optional, we can't choose whether to see a person or not once the signal travels from our eye to our brain, we only choose the label to apply (and even that's not much of a choice once the invariant representation is entrenched).
Since beliefs are stored as invariant representations, then yes, the concept of SR is an invariant representation.
Since our brain's pattern matching abilities work on the invariant representations already stored, then yes, changing those invariant representations would change the way we perceive reality. It would have to be a fairly comprehensive change though; because of the highly interlinked nature of invariant representations, changing one part may have vast repercussions. Our brain will let us know when our perceptions of reality don't match our invariant representations, and we won't like it at all if there's a huge discrepancy.
But that same nature makes it very difficult to change existing representations. We generally need a strong, or frequently repeated impression of something to form a solid invariant representation. And we need a stronger impression to then change it.
And the way neurons work means that when we change an invariant representation, we're actually replacing it, leaving the old in place, which gradually weakens due to lack of stimulation. That it's still there means it can be stimulated again and therefore provide competition for the new one (which is why habits are hard to change).
Anyway, that's my limited, lay person's understanding. Feel free to pick it apart and tell me if I'm wrong (while I go do some research to make sure I'm not just talking ♥♥♥♥♥