Legally, they don't need to choose. Section 230 limits provider liability for moderating user content and also limits provider liability for not moderating user content. I think the intent of Section 230 was to apply liability to the users making the content, not the service provider transmitting it; however, IIRC, cutrent jurisprudence makes it very hard to compell service providers to identify users in civil cases, so civil liability is hard to pursue, unless the user identifies themself in their content.

It's not a question of if they're a common carrier or nor; they don't need to be, and typically, they don't try to be.