New feature in the latest Mutable version:

Relay Storage Sync 🔄

Now, when you add users to your protected list or blacklist, this is encrypted and stored on your relays. This means you can visit Mutable from multiple devices (desktop and mobile, for example) and you’ll see the same information.

Note: This does not apply to your follow and mute list backups (yet), just your user preferences. (I plan to work on a way to maintain backups across devices soon, but that’s a bit more involved.)

https://mutable.top