Nothing is private on the nostr

absolutely possible, like your mute list is private, I don't know of a client that implemented it though

It is possible using something like listr.lol. But you will need to use a client that will display feeds of those lists, such as Amethyst or Coracle. Amethyst will only do so if at least one entry on the list is NOT private, though. I typically make my own npub that public entry.