What's so "extreme" about not wanting someone to advertise for a political candidate that you don't support on the property you own?
And the only one who carried it anywhere is her.
Because most people don't care that much. Especially if it is not effecting business.
Some people do. But since it is out of step with what the majority of people do it can be categorized as extreme.
Does not mean that it was bad, just means that it is not run of the mill. It is like the lady who repeatedly brought pork products into the company lunch room after she was asked not to. She was fired. People were screaming about that but it was their property so they were in the right. However the position is out of the norm and therefore it was a bit extreme.
BTW, she might have a case if, but only if, he allows other employees to have political tags on their car that are parked in the company lot. If it is a company policy then she has no case.