Copyright is created in the constitution. Once granted, it is a constitutionally protected property right. Equal protection and first amendment “control” but so does copyright. All must be given effect.

To use a different example: the government makes a law establishing yor back yard as a polling place for federal elections. Surely, you agree that peoples’ right to vote cannot to be vindicated if they can’t freely access polling locations. But that doesn’t mean that you are obligated to let everyone onto your property! The law is the problem, and the government is at fault for failing to ensure that polling locations are publicly accessible.