Urgh, yeah I've come across them before. I'm against them, in essence. Firstly, I don't even think the courses of action they recommend would even have any effect ("voluntarily phasing out reproduction"). I mean, in principle it's possible for everyone to just stop reproducing, but this seems intuitively unlikely. A better course of action to pursue for them or anyone interested in causing human extinction would be increasing x-risks in some way.
Also, it's predicated on biosphere survival being a good thing, I've made it clear in the past that I don't really think wild animals have very good lives, so the biosphere surviving is not, in and of itself, a good thing.
Sooooo, yeah, I don't think the mission they advocate is a good thing and I don't think their methods would even help them to achieve their goals.
World domination is such an ugly phrase. I prefer to call it world optimization