By default, anybody can interact with Muse in any channel (except for /config, which can only be used by members with permission to manage the guild).

To change this, go to Server Settings -> Integrations -> Muse and change the default permissions at the top:

Note that there's currently a bug where the default permission set by Muse for /config will not be reflected in Discord's UI. I recommend viewing the guild as a role to test permissions instead of relying on the UI.