Interestingly , I've never felt a huge variation of Cognitive Disconnance on a political issues where new information was revealed. I rather think logically them emotionally
It is important to remember that it is much easier to see cognitive dissonance in someone else than in yourself. When you go through cognitive dissonance, you aren't likely to be aware that it is happening - you believe you are rejecting the new information, simply because it is false, not because you want to believe it to be false.
It's fine to reject unsourced claims that seem false, but if given sources, it is generally worthwhile to critically examine them to see to what extent there is any truth in them.
The other side holds as well: when given unsourced information that seems true, it is worth investigating it as well to make sure your preconceived notions aren't leading you astray.