This is probably not even two cents, because evolution is not my field, but here's what popped off the top of my head.

Cognitive dissonance, if not dealt with, could have debilitating effects. Consider a child whose father says "I love you, Suzy" every day before sending her off to school, and then beats the crap out of her every day when she gets home from school. Suzy can look at the other kids and see that their parents don't behave that way, and yet all the other kids say their parents love them.

As a young child, peer acceptance is paramount, and loving, supportive parents, while not completely necessary, are a huge help in the socialization of a child. Suzy is faced with two logical choices:

1) Daddy doesn't love me.

2) Daddy does love me, but love has another definition for daddy.

Now, I know this is a flawed example, because we don't really have a definition of love, so don't sue me over it. Just follow the example, and I think you'll get my point. There IS a cognitive dissonance here. It's just not perfectly defined.

Anyway, if Suzy decides "Daddy doesn't love me," she's in a world of hurt. She hasn't lived long enough to understand that there is life away from the parents, or that the approval of her grade school peers will seem irrelevant in twenty years. All she can see is her entire future -- her whole life in front of her, without Daddy loving her. This choice is so terrifying, that it simply can't be real. (Of course, it is real, but Suzy has not learned yet that life bears her no will, good or bad, and she might just end up a quadraplegic tomorrow morning, and the world would march along, barely noticing.)

So, Suzy makes the only choice that fits her world model, and decides that her daddy does love her. Over the years, people will try to convince her otherwise. They will point out that he is an asshole to her, that he's never done anything but beat her, that other people's parents don't treat them that way, etc.. etc... but she will be unmoved. Before long, the decision will outweigh the consequenses. In other words, even after Daddy is dead or sent to prison, and has no other direct effect on Suzy's life, she will continue to profess that her dad loves her -- not because she needs his support, but because admitting her decision was wrong will force her to reevaluate her entire life based on the fact that she was so disasterously wrong about this important issue.

You can see how it can snowball... there could be many cognitive dissonances that would arise from her belief that her dad loves her, and she will make poor decisions on all of them because of that core belief. It will set up a cycle of cognitive dissonance.

*****

I know I haven't really answered your question. I've been describing a modern day scene, but I think it has relevance to evolution. Early childhood naivety is fertile ground for cognitive dissonance, and I suspect that it is linked to a child's perception of their parents as the "ultimate provider." We know that compliance to parents(authority) is something that is an evolutionary benefit for young. Cognitive dissonance, I believe, could be an example of that evolutionary trait gone slightly awry.

So, adults who have an easy time accepting cognitive dissonance perhaps learned early in life that sometimes A is true and false at the same time, and then continued that trend, while more skeptical minds either a) didn't encounter such scenarios, or b) encountered them later, or c) received guidance at an early age that helped them to overcome the tendency to rationalize A and Not A.

If you're interested, the idea of a "core belief" is central to cognitive therapy, which is gaining a great deal of support in the psychology community. The basic premise is that a cognitive dissonance causes a faulty "core belief" which in turn causes faulty decision making, and eventually, automated pathways form, so that the decision making process is bypassed, and the faulty core belief has caused a more or less permanent delusion.

I hope some of this has helped a little.