Facebook Inc. plans to exempt opinion pieces and satire from its fact-checking program, according to people familiar with the matter, as the social-media giant grapples with how to stop the spread of falsehoods while maintaining its own neutrality.

As part of the new rules, Facebook will allow publishers of information found to be false by outside fact checkers to appeal to the company, said the people familiar with the changes. Posts that Facebook deems to be either opinion or satire won’t be labeled as false even if they...