AFAIK, political speech is not protected against employer discrimination.
Increasingly, every single right that we have that was enumerated in the Constitution and the Bill of Rights has been encroached upon by the government via workarounds and loopholes (see: Commerce Clause).
While it’s all well and good to prevent the government from quashing speech and other rights, when your boss can fire you for saying something they disagree with or if you refuse things like workplace surveillance (potentially costing you your housing and healthcare in the process), these protections seem pretty threadbare. I think we need to do more to check the authoritarianism of our economy if we have any real aspiration to adhere to them.
1. I work for private company X.
2. X tells me to vote for Y, says that Y is awesome, supports Y, donates to Y. (pick any of these)
3. I campaign for and vote for Z.
4. I am fired because i voted for Z.
Any outcome in which X is not crushed into little pieces is so incredibly far off the deep end from what the values of who we are as a country are that it's frankly inconceivable to me. If the free expression of political speech is so crabbed and constrained that the above is ok, or legal, or both, then we're fucked.
Many people assume that gay and transgendered people are protected from employer discrimination but that is also currently being adjudicated.
If employers were unable to do anything about an employee's political speech, then China would face the choice between isolating itself economically, or tolerating criticism.
The correct play here, is to get the word out that people need to review every single paper they sign and line out the clauses that allow dismissal for bringing yourself or the company into public disrepute. People have to understand that they shouldn't be just signing away their rights like that.
The ACLU can't protect you if you've signed these kinds of contracts.