If your focus really is on a solution that is privacy friendly you should make use of a comment system you can host yourself on your webspace.
Comentario 3, Isso or Discourse (can be used as a commenting system only)
There are many more available. I haven't looked into all the other options yet but I will take a closer look at the other available systems some time soon.
At the moment I just use atabook and refer visitors to drop me a comment in the guestbook.
Having a privacy focused comment system that is hosted by a 3rd party would be dope but I'm unaware if there is any.
Waiting for other peoples recommendations