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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 contain information the fact-checkers determined was inaccurate, the people said.

The new rules follow Facebook’s acknowledgment last week that it will continue exempting politicians from fact-checks, on the grounds that such comments are newsworthy, as well as a recent controversy arising from a third-party fact checker’s determination that an antiabortion group’s video was false.

The rules, which haven’t been announced, coincide with Facebook’s decision last week to remove a false designation from a Washington Examiner opinion piece, overriding the conclusion of one of its fact-check partners. That op-ed argued that global-warming climate models have been inaccurate and that the risks of climate change is overblown.

The removal of the false label was celebrated by the CO2 Coalition, which employs the op-ed’s authors and argued in a letter to Facebook that the company had “used a partisan fact-check group to defame them.” The group, which receives funding from the oil-and-gas industry, dismisses global warming as a hoax and advocates for the “important contribution made by carbon dioxide to our lives and the economy.”

A Facebook spokeswoman didn’t respond to requests for comment on the new rules.

Together, the changes demonstrate the company’s continuing struggle to limit the spread of so-called fake news and other misinformation without being accused of stifling free speech.

“I know Facebook doesn’t want to be in the middle of this, but here they are,” said Angie Drobnic Holan, the editor of PolitiFact and a member of the board of the International Fact-Checking Network, which accredits Facebook’s fact-checking partners.

Ms. Holan said she expected that the changes as described would only affect the overall fact-checking program at the margins, but noted that publishers of false statements have a history of arguing that they are opinions.

“There are cases where the line between fact and opinion are not as bright as you might think,” she said.

Other fact-checkers have noted similarly slippery boundaries between fact and satire.

Rappler, a Manila-based news outlet that fact checks Facebook content in the Philippines, has documented bad-faith publishers dressing up false stories as satire. If such a dodge is allowed, Rappler wrote last year, “purveyors of fake news will now be able to escape accountability by simply labeling their stories as satire, no matter the intention, how badly written they are, how many clues they use to overrationalize, or even if they disregard every rule of satire.”

Facebook’s fact-checking program has become a central piece of the company’s response to misinformation since its unveiling in late 2016. Fact-checking groups choose what content to review, and material deemed false or partially false carries a warning and is distributed by Facebook’s algorithms to fewer people.

The program is limited to just over 50 groups world-wide, many of whom receive funding from Facebook.

The recent controversy over the fact-check of antiabortion organization Live Action illustrates the stakes. In a video distributed on Facebook, Live Action said that abortion is never medically necessary.

Science Feedback, a French nonprofit that was approved as a Facebook fact-checking partner earlier this year, labeled the claim false. Though Science Feedback’s conclusion was in line with medical literature and the primary professional association for obstetricians and gynecologists, Live Action alleged that the doctors who had consulted on the fact check were biased by their affiliation with abortion-rights organizations.

Live Action accused Facebook of suppressing debate, and the complaint was widely circulated in conservative media and eventually drew the support of Republican Sens. Ted Cruz and Josh Hawley.

Facebook removed the false designation from Live Action’s video, pending an investigation by the International Fact-Checking Network about whether Science Feedback’s actions were appropriate. On Friday, the IFCN said it stood by Science Feedback’s process and determination.

As of Monday afternoon, Facebook hadn’t restored the designation of Live Action’s video as false. The company also didn’t immediately respond to questions about whether the statement that abortion is never medically necessary might be classified as opinion.

A Live Action representative didn’t immediately respond to a request for comment.

Facebook’s fact-checking program has been panned by critics, and some partners have reported frustration over the limited tools provided to them.

Yet both fact checkers and the company have of late said the program is improving.

“I really appreciate that Facebook works with us to help find hoax content,” said Ms. Holan.

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