I think the field is called "epistemology", but I only know of the name; I didn't study it formally. I came up with this projection example myself, while looking for something more vivid than "focusing on different aspects", and this kind of clicked almost perfectly. In retrospect, it's not really original - I recall seeing suggestions like this in few places, notably the cover of the "Gödel, Escher, Bach", and some random Facebook meme. Also playing with shadows.

(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.