A twist on the previous question, would there be any way for me to deliberately choose to be completely ignorant of what I am serving, like running a Tor relay node (or like in Filecoin, if I understand that protocol correctly)? I would be a bit worried about the liability implications of having the ability to filter content I'm serving, but not having the time and resources to actually do any filtering.
As a non-lawyer, I would guess that you would receive the same safe harbor as ISPs do today: they can filter the content they serve, but don't until it's specifically reported to them, and aren't liable for those transmissions.
Even if, say, someone published a list of known illegally-transmitted copyrighted files, you could still make a strong argument that you don't trust the source of the list and would need to receive and review a specific report of each instance of copyright violation that went through your service, like the current DMCA model. (Again, though, not a lawyer.)