What is cognitive dissonance? (neurologically)

It’s like they feel no dissonance because of a mental wall. Instead, people around them experience the dissonance and discomfort when they try to understand that person’s contradictory points of view.

I either don’t follow or disagree. One person’s dissonance may be another person’s fine distinction, but in the case of the fine distinction person the confusion doesn’t exist. My curiosity is regarding what causes the confusion, not whether or not it would confuse one person and not confuse another.

What confusion are you talking about? Your confusion when you do not understand how someone can hold two beliefs you think or contradictory? Or when someone does not appear to be updating his beliefs in light of new pieces of information you believe are factual?

There’s the ads for pharms that depend on cognitive dissonance. The message they are required by law to broadcast is that the drug is dangerous, can cause liver failure, blindness or death, and those are the words used, but the image is one of riding bikes with the wind in your hair, lifting giggling grandchildren, and walking head on shoulder down the beach at sunset.
Unable to mesh these things the words are forgotten, as the visual brings bright emotions.

I mean a person’s inability to interpret facts that conflict with their prior beliefs. I’m not talking about MY opinion vs someone else’s opinion, but the assimilation of fact that conflicts with a person’s prior self-imagery.

This presupposes that there is some fact out there that does not come in laden with concepts and values. I am convinced (by what I think are excellent arguments) that this is simply not the case. So the fact that you believe you assimilate is simply not the fact that someone else receives, and thus, may perceive no conflict whatsoever.