Try to mute some user but it has a private profile

[codinghorror (Jeff Atwood)]

@JimPas

Edit: Have the user go to his/her preference, then click Users. A button is there to add a user to the Ignore list. Press the button and in the box They enter the username they want ignored or muted, then press Save Changes.

Yes, correct, you can do this from your own profile page, like so: