You can build this using 3Box, which has extended OrbitDB with DID-based access control system and user permissions. Check it out here: https://docs.3box.io/build/web-apps/messaging
3Box also has support for members only OrbitDB threads which can restrict posting to members, and encrypted OrbitDB threads to make posts private to the group. To Mark's point above.
That's intersting! In the case of persistent threads as mentioned in the link, can the set of moderators be mutable, and still have eventual consistency?
Yes, the list of moderators is mutable. It's addition-only out of the box, but to create a system where removing moderators is possible, you can create a new thread with the new set of mods (minus the one you removed) and the first entry in that new thread can reference the old thread. This model gives the new set of mods forward control, but the old content will still have the old set of mods.
This also works for encryption in members threads. To remove a member, you can create a new thread without the member and link the original thread. This gives forward secrecy since new encryption keys are generated for the new thread.
We're working on improving this system over time, but it requires some more advanced cryptography such as proxy re-encryption (like nucypher).
3Box also has support for members only OrbitDB threads which can restrict posting to members, and encrypted OrbitDB threads to make posts private to the group. To Mark's point above.