On further exploration (and please don’t take this as encouragement 
), I’ve found a few more options in the Preferences/User page.
Some people (like yourself) haven’t made their profiles public so you can’t access the option to Mute/Ignore them from there. However, it seems you can manage these options better from the Preferences/User page. 
You can even Ignore someone for a set amount of time.
Mute User is available from Trust Level 1, and Ignore from Trust Level 2. You can read more about how to attain those in Trust Levels.