I don't think that's necessarily inherent to right-wing-ism. Left wing politics has also had similar problems, and still does (say, organic food, or the way vaccine denial used to be a left-wing position), but it doesn't seem to dominate the position. Its bugaboos are "merely wrong"; they don't elevate to a movement-wide denial of well-understood sciences or a TV news network devoted solely to falsehoods about their opponents.
Perhaps that's just a way of redefining the terms of discussion: America's issue right now isn't really about right-versus-left at all, but about something else that happens to organize loosely along those lines. Perhaps rightism lends itself better to that, but I'd say that's inconclusive. Certainly left-wing-style thinking was the cause of a great amount of authoritarian violence in 20th century "socialist" countries. And we're left to argue whether that really is left-wing, or whether it's all just no-true-Scotsman.
You're assuming that they believe in the same sets of "real" and "fake" threats, or at least prioritise them similarly.