In Account settings under Interface a user can elect to select the option to “Hide my Public Profile and Presence features”.
However, this appears to cause an unintended effect as while the Profile can no longer be selected and will no longer show any information to other users whether signed in or not, the other users also can no longer interact with that Profile to either mute or ignore it. Effectively this option allows users to prevent their accounts from being muted or ignored by other users.
It may not be possible or easy, but the mute or ignore options should ideally be able to be interacted with on every user account, regardless of if the account in question has enabled the option to hide their public Profile.