For example, if you do illegal shit over the phone, the phone company is not responsible for your actions. The reason is that since they are not filtering or interpreting anything, they are not endorsing what you say. This is the "common carrier" idea.

I think this is a bad analogy.

The phone company user base is not a community. The phone company is nothing more than a utility. Reddit is not simply a utility or a platform, it is a community.

Internet communities and utility providers are inherently different, consider this exaggerated example: Reddit does not allow "sexual content featuring minors". I guess the reasons for that are a combination of resentment towards child abuse, and non-liability. Had Reddit tacitly allowed CP, anyone who distributed it on Reddit would still be a criminal. Reddit would be considered liable for allowing this shit on their platforms, but the ISP would be completely non liable.

Once Reddit takes a stance to ban (legal) topics, then allowing a subreddit to exist is basically making a value judgement that it's at the very least, "not as bad". There are actually quite a few subreddits that I think that Reddit would not want to "endorse" even in that very weak sense (I'm thinking of necrophilia and creepshots and other bad stuff)

Appealing again to the CP example. Do you feel, or think that anyone feels, that by disallowing CP Reddit is endorsing or condoning /r/gasTheKikes? Do you feel that by outlawing murder, the US endorses WBC? Everyone knows that there's always a (potentially huge) gray area between what you endorse and what you reject. This gray area is extremely important, because it is where norm shifts occur, but that does not mean that some extreme behaviors should not be excluded from it.

Now, suppose they do a housecleaning and clean out all that stuff. Should they still allow, say, /r/TheRedPill[1] to exist? Spacedicks?

Please see edit 3