From what I have heard and seen - there is a difference between moderating each message before it's posted - eg - classified ads person answers phone for local paper tells you that you can not advertise a tiger for sale or put 'foreman' wanted in ad - it must be gender inclusive.. is one type..
Then you have moderating where people can post about anything - but when you get a complaint you research and take it down.
There are other forms and types of moderation between these..
which is why I said "in this way could open"
if you are moderating each message before if goes out, you are not acting so much as a platform as more of a publisher.. you could claim you did not know that an ad you published was not legal.. say it was turtles for sale, or someone offering weed for sale with 'codewords'.. you could claim that you did not know the girl in the ad not in a sex tape, that you just published the info...
But from what I have seen, if you allow everything to publish and take down stuff when notified you have a difference situation in regard to section 230, and claims in general, as compared to having to defend that you ad person could of should of known before publishing..
Indeed - section 230 doesn't care so much about what is moderated out in some ways, but the fact you are moderating out 8 year old's dating profiles, but not 13 year olds could become an issue- and the fact that you moderated out the 8 year olds in the first place could cause holes in certain defenses.
So you would not be responsible for that isn't said - but the fact you allowed one defamatory thing to publish while hiding a defamatory post about someone else - what isn't said could be an issue to prove that you have liability for what is.
Hope I'm saying that right, again this is my understanding of some issues that I have been involved in, and studies other people's issues and listened to their counsel - but I am not a lawyer.. if you have one and you are doing this kind of moderating perhaps have them look into the backpage cases and see how they pierced the "we're a platform, not an editorial publisher' thing. for one example.