Defenders of slavery used that same "private enterprise" line to assert their rights over people; as did restaurant owners 100 years after slavery was abolished to justify kicking out people with offensive skin color.
It was not an existing law, but the ideal "that all men are created equal" which abolishonists and civil rights leaders pointed to in their quest for equality.
Likewise it is the ideal of freedom of expression which we are pointing to now that should protect humans from being banned from the digital town square for expressing offensive ideas.