Huh. That looks like really important context. I wonder why the Smithsonian article neglected to mention it. Do they just not want to admit that there's any dissent?
The Smithsonian article specifically mentioned it right after the leading paragraphs that outlined what the distinguishing features were and that it had been put forward:
The proposal was rejected by the international hierarchy of stratigraphy— of which the International Commission on Stratigraphy is a part— without citing substantive reasons, but most public criticisms of the Anthropocene stem from a range of sources: from within the heart of geology, to well outside it, among the social sciences and humanities.
It then goes on to address 10 points of dissent made and why these reasons are weak, misconstrued, not sufficient, etc.
I think the proposing team ran out of options on the formal track so now they're going the ad-hominem track against the IUGS (they're uncomfortable with the Anthropocene, they're climate-change deniers, etc.)