The problem with the second part of your argument is that you force me to pay, through my taxes, to a subway and then prevent me from posting things I want to say (but allow the other guy, because all he wants to do is sell soap).
By obviously you should have the right to not listen to a particular radio or tv show or not to look at a particular billboard. And yes, Fox News shouldn't have to argue points they don't want to.
But protecting you from seeing something you don't want to see? I don't want to see niggers, should the government lock them up?