Perhaps you're drawing the wrong moral. I don't know why it's generally important to predict disagreements, but I can think of other reasons the encounter could be, probably should be, profoundly disturbing.

If you take Robert Aumann's theorem seriously--which, put crudely, says you have no right to be cocksure of your position if your epistemic equals disagree--learning that some (perhaps numerous) intelligent, educated people have fundamentally different beliefs ought to induce (assuming you seek truth) serious doubt about your own views' accuracy. Maybe the reactionaries are correct! Or more seriously, you have acquired (assuming many similar others exist) strong evidence tending to show that you're as wrong as they.