(Note, do not confuse this example with the infamous "9 / 6" meme, with two people standing over a number painted on the ground and claiming they're right. One of them is wrong, because there's no information loss giving degrees of freedom here; the digit was drawn with a particular orientation in mind, and one party is ignoring it.)
The intended implication of my example is that if political (or other) opinions are necessarily projections of the full issue, you probably need to hold more than one at the same time. Consider technical drawings, e.g. CAD drawings of parts. In order to completely describe a physical part, you almost always have to have multiple projections on a single picture. I believe the same applies to understanding the real world - which is why I like to listen to "the other side", and generally hate the concept of taking a side.
I have the very same feeling, this concept seems near perfectly correct, which is why I'm trying to find some formal discussion of it, something with more meat on the bone.
Did you come up with this way of looking at it, or is this from some sort of a dedicated "field of study"? This seems to me an extremely good description of what's going on in society lately, from fake news to disagreement on a wide variety of issues, and perfectly explains why opposing sides both think they are right - because often they are both right, they've just chosen different perspectives (subsets of dimensions) for their lower-dimensional conceptual understanding of the larger high-dimensional problem. Throw in the low precision, low dimension capabilities of language and communication, a lack of intellectual humility, and you've got the perfect recipe for a complete gong show even if everyone is trying to be honest.