Take the parallel postulate. It holds in Euclidean geometry but not in others. Am I an idiot for not using that postulate (and its implications)? No, I'm starting from a different set of assumptions than someone studying Euclidean geometry. As a consequence I'll reach different conclusions than someone studying Euclidean geometry.

Neither of us are idiots, we both know what we're doing. The conflict is when I make an assertion about geometry (general) that doesn't hold for geometry (Euclidean) (or the reverse, the other person makes a general assertion that doesn't hold for non-Euclidean geometry). Unless we sit down and compare our base assumptions (axioms), we cannot resolve this apparent conflict.

I'm not saying this is universally the case, there are contrarian trolls and idiots out there, but oftentimes people are reasonably rational but are starting from different positions. This leads to conflicts in politics, economics, religion, and, yes, the understanding of the physical world. It's not helpful to call them all idiots because many times they aren't, they just have different base assumptions (or priorities, often, in the case of politics and economics). And calling them idiots only leads to an emotional, not rational, "discussion". Take a step back, don't be a jerk, and listen to them, work backward to the actual point of disagreement and then focus on it (or not, once discovered you may realize there is no resolution that will satisfy either or both of you).