Social media companies don't become more liable just because they moderate. They all do that already. There's no sudden legal line between moderation involving messages with spam or bigotry.
I think anyone amplifying messages on a large-scale in a one-to-many manner, between people that aren't equally engaged in a conversation together, should be considered to start accruing responsibilities over the content of what they're participating in amplifying, in a way that a phone companies largely don't have. I think social media companies have been largely shirking that responsibility by phrasing it as a free speech issue and letting anything go.