Check the text yourself [0] there's nothing in there about having to either be a complete free zone or even to moderate neutrally to get protection from civil liabilities. Personally I wish they'd take a tougher stance but legally they don't have to and I /really/ don't think it's a good idea to legally require them to because the definition of what is and isn't moderation worthy will change on a dime. [1]
[0] https://www.law.cornell.edu/uscode/text/47/230
[1] Especially under the 'unitary executive' theory which is used a lot to try to undermine any congressional restrictions or accountability on the executive branch. That means the interpretation and enforcement can and will switch overnight every 4-8 years.