A good example of cognitive dissonance is if I encounter evidence supporting the truth of evolution, against the background of my basic desire that evolution be false.
Another good example of cognitive dissonance is if you encounter evidence refuting the truth of evolution, contradicting your wish that evolution be true.
In scientific terms there's no "truth" in evolution because the word "truth" is reserved for philosophy and religion.
There is also no "proof" of theories since "proof" is reserved for courts of law, mathematical theorems and, of course, whiskey.
Instead, what can be observed is called "fact" and any hypothesis is confirmed or falsified by its ability (or lack of) to predict previously unknown results.
So consider some very strongly confirmed theories, such as gravity.
What happens when we hear of supposed UFOs said to defy gravity?
Do we imagine suddenly that the laws of gravity have been repealed, or don't work, or are now falsified?
Maybe, but first don't we question if those alleged sightings are really what was claimed?
How certain are we that those fuzzy photos really are Koozbanean Fazoobs and not just evolving Phoobs?