Some of Republican presidential candidate Donald Trump’s posts on Facebook have set off an intense debate inside the social media company over the past year, with some employees arguing certain posts about banning Muslims from entering the U.S. should be removed for violating the site’s rules on hate speech, according to people familiar with the matter.

The decision to allow Mr. Trump’s posts went all the way to Facebook Inc. Chief Executive Mark Zuckerberg, who ruled in December that it would be inappropriate to censor the candidate, according to the people familiar with the matter. That decision has prompted employees across the company to complain on Facebook’s internal messaging service and in person to Mr. Zuckerberg and other managers that it was bending the site’s rules for Mr. Trump, and some employees who work in a group charged with reviewing content on Facebook threatened to quit, the people said.

Mr. Trump’s campaign didn’t respond to requests for comment. In a statement provided Wednesday evening, a Facebook spokeswoman said its reviewers consider the context of a post when assessing whether to take it down. “That context can include the value of political discourse,” she said. “Many people are voicing opinions about this particular content and it has become an important part of the conversation around who the next U.S. president will be.”