The Constitution limits the government's—including government employers'—power to discriminate based on race, sex, or religion. A federal statute and statutes in nearly all states applies these norms to private employers as well. Many libertarians disapprove of any such restrictions on private employers; but for nearly 60 years, American law has imposed such restrictions.
The Constitution also limits the government's—including government employers'—power to restrict people's speech and political activity. And statutes in many states apply this norm, to some extent, to private employers as well. Indeed, a few of them have done this for 150 years (and even longer as to employers' discrimination against employees based on how the employees voted).
Ten years ago, I wrote a descriptive and analytical law review article called Private Employees' Speech and Political Activity: Statutory Protection Against Employer Retaliation, which aimed to catalog these often-little-known statutes. This year, I'm returning to the subject, trying to analyze the strongest arguments for and against such statutes. The article (Should the Law Limit Private-Employer-Imposed Speech Restrictions?) will be published later this year in a Journal of Free Speech Law symposium issue, together with other articles that stemmed from an Arizona State symposium on Non-Governmental Restrictions on Free Speech; and this week and next I'd like to serialize it here.