And in fact, you cannot stop me from putting leaflets on your car, no matter how distasteful you find the content, just because it's your property. In fact, in many jurisdictions, putting stickers is allowed too, the line being drawn at damaging the property of someone else. (I can write stuff on your car with easy to wash water paint, but I can't carve a message on it).
> If you ran a bookstore, and I could force you to carry a bunch of books that glorified Nazism
Welcome to the life of every bookstore clerks in the world. And it turns out they aren't allowed to remove books they disagree with, nor add their own favorite book in the store. If the owner of the store can force that on its clerks I see no reason why the legislator couldn't do the same on the owner. In fact, in countries that aren't hypocritical about freedom of speech, you cannot get fired by your boss if they dislike what you say, but you can definitely be fired if you refuse a customer, which shows doing business has nothing to do with freedom of speech.
So at the end of the day, having refuted your two arguments, my point still stand: Doing business isn't akin to speech, and corporations aren't human beings in the first place so they shouldn't be entitled human rights anyway.
Also, property right isn't some special kind of right that trumps everything else, it's one basic right like any other and have no precedence/superiority over the others.