“I doubt very much that they would take a drastic action like cutting him loose,” said Mike Shatzkin, the chief executive of Idea Logical Company, a book industry consulting firm. “They’re not going to die if he’s not there, but they certainly would be scrambling to make up the revenue.”

A publishing house is not subject to the same pressures as a network, which depends on advertising revenue, but occasionally a public scandal will drive publishers to drop an author. Simon & Schuster faced a fierce backlash this year from independent booksellers and some of its own authors after it bought a memoir by Milo Yiannopoulos, a former editor at Breitbart News who espouses views that many regard as xenophobic and misogynist.

His publishing contract was canceled in February after a video clip resurfaced, in which he condoned sex between adults and teenage boys. By then, the publisher had suffered a public relations debacle.

Even if Henry Holt continues to publish Mr. O’Reilly, his sales could fall as a result of the allegations against him, particularly if major book retailers decide not to carry his titles, or Fox cancels his show. His children’s book series, a spinoff of the “Killing” books, could be particularly vulnerable to a consumer or retailer boycott, given the nature of the allegations. “Give Please a Chance,” a picture book he wrote with James Patterson, has sold 181,200 copies since it was released in November, according to NPD BookScan.

Then again, the allegations against Mr. O’Reilly could lead his most loyal fans to double down on their support.

“The people who like him may be even more inclined to support him now and vote with their dollars to say, ‘I’m with you, Bill,’” said Michael Cader, the founder of Publishers Marketplace.

So far, major book retailers are sticking by him. “We leave it to our customers to decide what to buy and read,” a Barnes & Noble spokeswoman said. Amazon, which declined to comment, features “Old School” in its spring reading nonfiction recommendations.