Of course, if the employer has any sense at all, they will usually try to find a way to get rid of the employee that hides the objection to that employee’s outside activities. HR in a company of +100 tends to be very adept at finding ways to show you the door.
But we do not live in a frictionless vacuum, where they saying of things comes without consequences. Some of those consequences are salutary, and some can impact us very hard. Because, what is the point of expression that amounts to but shouting into the void? If you are not ready to deal with the effects, then STFU.
The OP’s first example is interesting. In general, most employers aren’t going to get pissy if you go put a political candidate’s sign in your yard, or even some kind of political/religious statement. My experience is that they get concerned when the employee’s out-of-work behavior is likely to reflect badly on the company in some way. So if you’re out there doing stuff that’s drawing attention to yourself, your message, AND is something that can come back to reflect on the company, then they’re going to be pissy about it and possibly fire you. So if your pro-choice sign is 10 feet tall with flashing lights and a loudspeaker, and you’re on the news as “John Doe, owner of the sign and employee of XYZ corp” they would probably not like that.
But if your sign isn’t anything remarkable, then it’s unlikely they’d know or care. It’s the uncontrolled involvement of the company that the vast majority object to, not that their employees have different political opinions than the company line.