Just because conservatives could be more likely to consume false information, doesn't mean the other side is not spreading disinformation.

For example, your comment could be a piece of misinformation. Did you read the book from the first link you posted or are you just quoting an article which is qouting a book. Did you read the second study, or just the article. A lot of times spreading misinformation is not fabricating lies, but just hiding the truth. People will take a study or an another piece of information and extract only the things that benefit their narrative.

The best example that I have is the wars during the breakup of Yugoslavia. I personally lived through some events there, I know everything that happened during those events, but when I look up those events on the internet different information is missing, based on the nationality of the writer. Each side is trying to paint themselves as right and ommits information that hurts them.