That's true. It says "Congress shall make no law", and that is understood now to also apply to the states.
IMHO one of the biggest failings of libertarian theory is the treatment of private entities when they become de facto governments. Libertarians believe government should be tightly constrained (or absent entirely in the case of libertarian anarchism), and businesses/corporations should not be regulated beyond making sure they do not violate the non aggression principle. But what happens when a corporation becomes so dominant that it itself begins to encroach on what are commonly considered the rights of individuals? Google, FAcebook, et al have the power to pick and choose who gets to speak freely and who does not on their platforms, which is not a big deal when there is sufficient competition, but what happens when those companies reach a position of dominance in social interaction and begin to have an effect on the ability of people to express themselves? A good example would be FAcebook or Twitter blocking accounts that certain groups use to coordinate meetings, demonstrations, and the like. Stuff like that is just starting to happen.
I don't think the Googles of the world have quite reached the point where the government needs to step in (and the staunch libertarian in me hates that idea), but we are approaching that point, particularly in light of how other entities such as banks and payment processors are refusing to do business with entities engages in perfectly legal endeavors such as gun sales. That door is already open WRT so called public accommodation laws that force businesses to cater to everyone, not just those they want. My feeling is that is a violation of association, so it's not a simple answer.