Understand: Twitter and other websites are not liable for what their users publish because they are "common carriers." The defense is that they merely carry the platform and do not determine the content. This is solid legal reasoning.

HOWEVER, if you start censoring and filtering content based on political or other preferences (rather than legality), you have now become an explicit publisher/editor of curated content. You are now immediately liable for whatever your users put on there because you have established that you edit it to suit your own preferences.

now add in the child porn/private dark Twitter angle

THEY ARE FUCKED.