If you don't know about it, then no, according to https://en.wikipedia.org/wiki/Cubby,_Inc._v._CompuServe_Inc. (This is one of the cases that spurred Section 230; the analysis is, I believe, still valid today for sites that don't moderate things, because the point of Section 230 was to provide equivalent protection for sites that do moderate things. But it's definitely valid if Section 230 goes away.)

I think it's the opposite. If you don't moderate you are not responsible. If you moderate, you undertake liability.