We may never know. But here's what I suspect: maybe they don't experience cognitive dissonance at all. Many Trump supporters, like Trump himself, don't seem at all interested in any kind of rational consistency; it's all fear and emotion and gut feelings and hatred, and they latch on to any argument that superficially seems to justify their hatred, completely oblivious to the fact that their argument would hurt their own candidate even more.

It's only a theory of course; I can't look inside their heads. But the lack of consistency is clear.

notoothpaste is a Trump supporter. He's accusing you of cognitive dissonance.

His comment works better the other way around.