No, the original Freenet was more like a decentralized dropbox, not a general purpose decentralized computer like the new Freenet.
> but do I really want to serve as a host for CP unknowingly? I guess it might be possible to block known unsavory content, but that just seems like an endless game of cat and mouse.
The new Freenet will have a reputation system that will strongly punish anyone's reputation for posting anything like CP. Also, when your computer is part of the (new) Freenet network, it acts more like a relay than a host.
> Anonymity is way more important than resilience.
For some things, not for others. That's why anonymity with the new Freenet will be a service, not built into the OS itself.
> Can you explain the reputation system a bit more?
While it's still at the conceptual stage, the reputation system would be a generalization of a system called "web of trust" in the original Freenet [1].
> Is all content in freenet public or how would you know that someone posted certain content?
It depends on the system. For example, something like a forum might have minimum reputation requirements for posting, and also the requirement that the forum can downvote your reputation if you behave badly - this being the punishment.
> Do other users actively have to "down vote" them to reduce their reputation or is there an entity which can influence reputation?
It's a decentralized mechanism so it's all based on user feedback, but with web of trust it's transitive, so downvoting you may also downvote those who endorsed your reputation.
But bots can also participate, for example a bot could use modern deep learning to identify objectionable material and downvote automatically.
> Is there are single global reputation system or is it more local?
It's a mixture - trust is transitive so proximity matters but it isn't just about your immediate trust relationships.