This opinion piece was first published by The Wall Street Journal.

It’s the classic threat of B-movie mobsters: Nice business you got there, it’d be a shame if something happened to it. Government shouldn’t operate like that, but it too often does, sometimes to evade the Constitution’s limits on its power. A recent decision by the Second U.S. Circuit Court of Appeals upheld the practice and provided a road map for officials to circumvent the First Amendment’s protection for freedom of speech.

Maria Vullo led the New York State Department of Financial Services, which has broad power to regulate almost every major financial player in the U.S. After the February 2018 school shooting in Parkland, Fla., Ms. Vullo and then-Gov. Andrew Cuomo issued a press release stating that the department would “urge” the insurers, banks and companies it regulates “to review any relationships they may have with the National Rifle Association” for “reputational risk.”

The goal was to punish the NRA for its gun-rights advocacy. The press release quoted Ms. Vullo as saying that corporations need to “lead the way” on “positive social change . . . to minimize the chance” of future shootings. “DFS urges all insurance companies and banks doing business in New York to join the companies that have already discontinued their arrangements with the NRA.”

Ms. Vullo followed through with official guidance to regulated entities. Citing “the social backlash against the National Rifle Association” and society’s “responsibility to act,” the guidance directed insurers and banks to evaluate the “reputational risks” of “dealings with the NRA or similar gun promotion organizations.”

Behind the scenes, Ms. Vullo was pressuring senior executives of the insurance syndicate Lloyd’s of London. In 2017 she had launched an investigation of insurers that formed partnerships with the NRA to sell “affinity” insurance, including gun-owner policies. The basis was twofold: technical violations of disclosure rules and alleged violation of state law by covering losses, including criminal-defense costs, even when policyholders were found to have illegally discharged their weapons.

The NRA alleges in a lawsuit that, in a meeting with Lloyd’s, Ms. Vullo acknowledged that these problems were widespread in the marketplace but made clear that her focus was the NRA policies. The key to minimizing liability, she emphasized, was joining the department’s efforts to combat the availability of firearms by weakening the NRA.

Lloyd’s got the message. Despite its reputation for insuring even the most controversial risks, it understood that its regulator considered working with one of the nation’s most broadly supported advocacy organizations to be off-limits. Lloyd’s publicly announced that it was terminating all business with the NRA. It signed a consent decree with DFS permanently barring it from participating in any insurance program with the NRA—rather than the usual remedy of bringing policies into compliance and possibly paying a fine. The decree didn’t cover the non-NRA policies that ran afoul of the same New York laws. The NRA says its corporate insurer refused to renew its policy because it feared similar reprisals after seeing DFS target Lloyd’s and another NRA-affinity insurer.

In Bantam Books v. Sullivan (1963), officials from the Rhode Island Commission to Encourage Morality in Youth sent letters to booksellers informing them that it had identified certain books and magazines as “objectionable” and noting its power to recommend obscenity prosecutions. The U.S. Supreme Court held that this “informal censorship” violated the First Amendment. Although the government didn’t seize or ban any books, it “deliberately set about to achieve the suppression” of protected speech.

So did Ms. Vullo. As the Second Circuit observed, she “plainly favored gun control over gun promotion” and therefore “sought to convince DFS-regulated entitles to sever business relationships with gun promotion groups.” Yet the judges concluded that was reasonable.

Their logic is circular: The NRA’s advocacy led to a “backlash” that could “affect the New York financial markets,” given that “a business’s response to social issues can directly affect its financial stability in this age of enhanced corporate social responsibility.” So Ms. Vullo’s entreaties to drop the NRA weren’t threats, but actions “to protect DFS-regulated entities and New York residents from financial harm and to preserve stability in the state’s financial system.”

It’s fanciful to suggest that selling insurance to, or in partnership with, the NRA poses a threat to New York’s financial system. More important, the Constitution’s protections don’t amount to much if government officials can censor disfavored opinions simply by labeling them “reputational risk.” And even if such risk is real, empowering government officials to engage in censorship on that basis creates a heckler’s veto over controversial speech: Gin up enough online outrage or disagreement by officials or purported experts, and you can justify censoring anything or anyone.

The Biden White House successfully pressed Twitter to shut down accounts, including journalist Alex Berenson’s, for bucking the expert consensus on Covid vaccines. The FBI and Twitter cooperated in 2020 to censor humorous tweets about the election and voting. The Cato Institute’s Will Duffield has identified 62 recent instances of government officials making specific demands to censor speech on social-media platforms. This kind of “jawboning” by government officials usually occurs in the shadows and rarely comes to light. It can be difficult to identify when official encouragement crosses the line into coercion.

The Supreme Court will have to take up the question sooner or later, and an NRA appeal would present a strong opportunity to do so. The DFS has broad discretionary power to regulate industries on which almost everybody depends. That makes it all the more crucial to ensure that it respects the Constitution.

Mr. Rivkin served at the Justice Department and the White House Counsel’s Office in the Reagan and George H.W. Bush administrations. Mr. Grossman is a senior legal fellow at the Buckeye Institute. Both practice appellate and constitutional law in Washington.