It just seems a bit dodgy to me that an adult can be told by their boss what they are and aren't allowed to talk about.
Doesn't it? But it's ultimately derived from the Constitution.
Employees and employers have the right to contract restrictions on constitutional rights. An active ATP professional tennis player who doesn't allow himself to be tested for drugs at will, can be banned. A football player who yells obscenities at his coaches or the referees might be able to have his contract voided. A TV personality discovered to have said off-air at a public forum can be fired.
Free speech isn't unrestricted. A union or an individual who accepts a contract to work (employment), is subject to all "legal" conditions an employer requires. You can't decide to not wear a uniform or to not maintain reasonable hygiene, for example, if wearing a uniform and maintaining reasonable hygiene was a requirement for employment. You can't decide to not answer phones (if you're hired in part to answer phones), can't decide to not sell guns (if you are a salesperson in a gun shop and hired to sell guns), and then claim your Bill of Rights are being violated.
Of course, by law illegal acts are void in contracts. You can't require things that federal or state laws already prohibit. But the constitution, afaik, doesn't recognize contracted restrictions on free speech as illegal. It's a right people can agree (implicitly, explicitly), to give up as part of the employer-employee bargaining relationship. The NLRA seems to mean as much.
Anyway, that's my take, although I'm neither a lawyer nor judge, from reading and discussing those issues with people who are in the labor and legal fields.
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