If she's parking in his parking lot I guess he has every right to not want he political advertising on his property...and she has every right to find another job.
It is a bit of a gray area as her car is in the parking lot which is company property however it is rather rare for an employer to do this. The sticker would usually have to be an egregious violation, something that would reflect badly on the company as a whole.
There is ample support for saying that you may not wear political clothing at work but a bumper sticker? I would say that there is a lot more to the story then is being told.
Her comment, "You can't tell me who to vote for!" is very odd. How does that leap happen?