The complaint that the term is anthropocentric is naturally a consequence of correlationism, which holds that one can't access things directly, but only through some kind of correlation (such as the (human) subject etc.).
The Kantian meme has propagated through scholarship and opinion very well: evidence is precisely the dislike of the term "Anthropocene," which names a time that began exactly when Kant was writing.
I see these two facts as what Adorno would call two halves of a torn whole that don't add up together.
Speculative realism gets a strange boost from the debate about this term. Scholars who are not aware of what has happened in philosophy are now having to grapple with the same sorts of issue: whether or not we can access it, there is a reality that is mind independent and (human) culture independent.
The intensity of the allergic reaction against this idea underlies the reaction against the term "Anthropocene."
The quilting point is precisely the human insofar as the human is now a geophysical force on a planetary scale. We are now compelled to see ourselves as actors in and on the real, not simply correlators or measurers or perceivers or PR people.
The term "Anthropocene" reinserts what was unconscious back into humanities scholarship: the human as a real agent, in the real. And in an awkwardly PC way: who can deny that modernity was toxic, at this point?