There is no "privilege". All 230 does is stop the US court system being abused. It specifies two key things:
1) If you don't like something someone says on Twitter you have to sue that person, not Twitter. That seems obvious to us in the UK but is not what normally happens in the US: in the US you don't sue the person responsible, you sue the person with most money! As the US court system is so expensive and so unpredictable, everyone prefers to sue companies with deep pockets as they are more likely to just settle and there is a chance of getting a massive payout. 230 forces people to sue the person who wrote the tweet instead, meaning many, many fewer cases.
2) If Twitter moderates your tweet, they can't be sued for their decision. That is the only thing that keeps Twitter from being much, much, much worse. Without that protection, Twitter will have a moderation policy that just says something like "we take down tweets that are terrorist or child porn related and that is it" and will not be able to delete anything else.
Even worse, the very biggest social media companies can afford enough lawyers, and large enough moderation teams, to maybe handle life without Section 230. But there will never be a new social media company: no startup can live with these two changes.
With the current law, if you want to create a right wing or left wing social media company you can do it. And when it becomes big you can use it further your views. But with these changes, this is it. You can't grow a new social media company so we are all stuck with whatever the views are of Twitter, Google, Facebook.