No. NIP-51 clearly defined that private mute list (tags) should be encrypted in "content" event field

https://github.com/nostr-protocol/nips/blob/master/51.md#encryption-process-pseudocode

Amethyst for example has done that properly by encrypting the tags in content field

https://github.com/vitorpamplona/amethyst/blob/bb0d8f186b687e14c256fc1e10149823e7c6e512/quartz/src/main/java/com/vitorpamplona/quartz/events/MuteListEvent.kt#L64

AFAIK, Snort support both public and private list. Block button for private list and mute button for public list.

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> mute button for public list

And that's how you get caught muting.

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.