This post is me trying to get my head around the different terms used by Herbrechter in his interview (see link above). I realize I’m over simplifying; Philosophy is not my strong subject.
To understand the term “Critical Post Humanism”, I need to know how Humanism is defined; it seems to be the belief that human dignity, interests and values are of primary importance. Humans are special. Although there are many other definitions I think this is the one that Hebrechter is alluding to.
The Post Humanists believe we are heading towards the end of Humanism or starting an era after Humanism. They are critical of humanism in light of recent abhorrent world events, imminent environmental disaster, advances in life science (animals are pretty clever too), and advances in technology. I think they also disagree with the idea of humans being categorized as a single entity, as humans by their nature are so diverse (could be wrong on that).
The Post Humanist comes in many forms, the most far out being the Transhumanists, they believe that technology can make us more human (more special), through enhancement using technology to improve our physical and mental abilities. This would include the (once SciFi only) practices of cyborgisation and prosthesisation, as well as prolonging life etc.
So that leaves us with Critical Post Humanism, the critical post humanist believes as other Post Humanists, that we are at the end of the Humanist period, or start of a new period after Humanism, but is not prepared to throw away everything that humanism stood for. There were some pretty good things like equality, justice etc. While their attitude towards Transhumanism is open, and they’ll take it on a case by case basis.
Or at least that's how I understood it.