In a way cognitive dissonance is the opposite of intellectual honesty. So the cure for cognitive dissonance is to be intellectually honest.
Enjoying your eggs for breakfast does not mean you approve of the unethical treatment of animals. Nor does the duck a l'orange you have for dinner. Nor does that make you a hypocrite when you send your donations to the Animal Humane association or support the candidate who promotes laws for the ethical treatment of animals.
Re the corrupt politician, the intellectually honest will ask himself/herself, "Do I KNOW this person is guilty of crimes? Have I seen the evidence with my own eyes; heard it with my own ears? Or has he/she confessed to the crimes? Or has he/she been found guilty with due process in a properly conducted court of law by a jury of his/her peers?
Or do I believe he/she is guilty because I heard talking heads on television--people who hate the person--tell me he/she is guilty? Do I believe it because I dislike this person and want to believe it?
The intellectually honest will admit the truth once he/she arrives at it. The cognitively dissonant will not.