It is a gray area and social media platforms sit somewhere in-between being a common carrier and a being a publisher. Your right there is no hard legal line but the more they decide what is allowed and what is not allowed the more they move farther away from being a common carrier.
> Social media companies don't become more liable just because they moderate.
It appears that those links describe the conditions before passage of the communications decency act of 1996. That was all overturned by section 230 of the CDA.