A strange example, but okay, I'll play. Okay, say a private property owner wants to have a gay orgy in his house. A condition of attending the party is that you have to engage in homosexual sex while there. If not, you will get booted out of the party. If you refuse to engage in homosexual sex, can the owner of the property deny you an invitation or kick you out? Of course.
A private entity can no more strip a person of their inalienable Rights than the Government can.
Your rights have not been stripped. You are not forced to work for a particular employer.
If it was a rally inside my car, sure. It'd be an awefully small rally though.
So, as long as you are sitting in your car, you can violate your employer's rules? That is just a ridiculous position.
When my employer holds the pink slip to my car, then they can dictate the contents. Period. End of story.