Social media can be a public minefield for employers, requiring them to develop and implement practical, enforceable social media policies while also carefully considering when to discipline employees for violating those policies.

While employees terminated by private-sector employers generally would struggle to successfully argue that the firing breached First Amendment free speech rights, they could pursue other claims such as gender bias against their employers in some circumstances, experts say.

“A very good question to ask is why are we talking about social media in the workplace?” Joane Wong, New Yorkbased senior attorney with the National Labor Relations Board, told attendees of the American Bar Association’s annual Labor and Employment Law Conference in Washington last month. “That’s how we communicate these days. We no longer just talk to our co-workers face to face or pick up the phone. Instead, we type out our concerns and press send, or we post something or press ‘like.’ Now we have people pressing buttons, and everything’s written out and is discoverable.” 

In a recent example of the implications social media has for the workplace, a cyclist was fired after posting a picture of herself “flipping the bird” to President Donald Trump’s motorcade. According to news reports, Juli Briskman, who oversaw social media for Herndon, Virginia-based government contractor Akima L.L.C., raised her finger in an obscene gesture to the Trump motorcade on Oct. 28, then posted a picture of it on her Facebook and Twitter accounts, which were later widely disseminated. She did not identify herself as an Akima employee.

Legal experts generally agree that she does not have a First Amendment case against her former employer. They point out that only a handful of states — which do not include Virginia, where Akima is based — would offer employees protection in such a case.

“They fired her legally,” said Eric B. Meyer, a partner with Dilworth Paxson L.L.P. in Philadelphia. “Virginia’s an at-will employment state, and as far as I know she was an at-will employee.” 

“They could have any reason or no reason at all to get rid of her,” but in this case she violated the firm’s social media policy, “so that gilded the lily, so to speak,” he said.

Employees use social media “at their peril,” said Richard B. Cohen, a partner with FisherBroyles L.L.P. in New York.

Ms. Briskman said, according to reports, that although she was fired for her action, another male employee of Akima who had posted objectionable content about the Black Lives Matter movement was permitted to retract his comment and keep his job. Arguably, she could pursue gender discrimination charges because the male employee was not terminated after his offensive posting, although experts say she would likely have an uphill battle.

“You could make a claim in this case that she’s being discriminated against because she’s female,” which could rise to a gender discrimination claim, said J. William Manuel, a partner with Bradley Arant Boult Cummings L.L.P. in Jackson, Mississippi.

“If I were that company’s lawyer, I’d be a little nervous about a potential gender discrimination claim because the female was treated so differently,” said Aaron Goldstein, a partner with Dorsey & Whitney L.L.P. in Seattle. A likely defense, he said, is Ms. Briskman could have damaged the firm’s business as a government contractor.

Ms. Briskman’s situation is comparable to workers who were fired after their employers learned of their attendance at a white supremacists’ rally at Charlottesville, Virginia; the situation involving James Damore, the Google Inc. engineer, who was fired after criticizing the company’s diversity efforts; and National Football League players who kneeled during the national anthem, experts say.

Colin Kaepernick began kneeling during the national anthem in 2016 in protest of the treatment of minorities in the United States, a movement that accelerated across the NFL when President Trump tweeted his opposition to the protests. The protesting players initially received the support of several of their employers, though some NFL owners later criticized their stance.

Mr. Damore was fired from Google in August after writing a memo in which he suggested that women are less biologically suited to work in the tech industry than men, portions of which the Mountain View, California-based technology company said violated its code of conduct.

But employers must consider whether such discipline or action creates an even bigger problem, Melinda Burrows, senior legal director with software company NetScout Systems Inc. in Westford, Massachusetts, said at the ABA conference. Ms. Burrows said she “always starts with the ‘so what?’ test. How big a deal is this really? Is it content that requires you to react?”