It is not /meant/ to be private at all. The priority here censorship resistance, just like Bitcoin. Now given censorship resistance, you can work on privacy and security, or at least thats how I've constructed it in my mind.
From Vitor's Amethyst repository:
> Privacy and Information Permanence
Relays know your IP address, your name, your location (guessed from IP), your pub key, all your contacts, and other relays, and can read every action you do (post, like, boost, quote, report, etc) except for Private Zaps and Private DMs. While the content of direct messages (DMs) is only visible to you and your DM counterparty, everyone can see when you and your counterparty DM each other.
If you want to improve your privacy, consider utilizing a service that masks your IP address (e.g. a VPN or Tor) from trackers online.
The relay also learns which public keys you are requesting, meaning your public key will be tied to your IP address.
Information shared on Nostr can be re-broadcasted to other servers and should be assumed permanent for privacy purposes. There is no way to guarantee the deletion of any content once posted.
And Mike Dilger's Gossip:
> Privacy Options: in case someone wishes to remain secret they should use Gossip over Tor - I recommend using QubesOS do to this. But you could use Whonix or even Tails. Don't just do it on your normal OS, because on a plain OS sometimes data leaks around Tor (things like DNS lookups). Gossip supports using native TLS certificates so you can configure trust for .onion sites. Gossip provides options to support privacy usage such as not loading avatars, not loading images, not necessarily sharing who you follow, etc.