Voting is secret, so no. But if you blog about how you vote, and your employer googles you? Employment law varies by state, so it’s tough to generalize. But plenty of people have been fired for ill-advised Facebook posts and pictures.
Privacy is a good thing!
Stein’s lawsuit will probably be dismissed. But “I was fired because I don’t believe in Global Warming” helps improve his “Brand” as a conservative writer/lecturer; IOW, the lawsuit is likely a publicity stunt.