Yes, there is two options. Damus implement public mute list. Amethyst private list (buth can adapt to existing public list) and Snort can do both clearly. Depend on Clients.

>Even the content was encrypted, the "tags" remains unencrypted.

NIP-51 defines that clearly.

>Unfortunately i do not see a client that has option to not publish a mute list publicly.

Snort have both options.

My reply above for your statement in this claim. Which is not true.