The best part is "all remaining creatures will be free to live, die, evolve (if they believe in evolution)." From that, I gather that if a creature does not believe in evolution, it cannot evolve? Heh.
Seriously, though, the movement is interesting in concept. They're not proposing to extinct the species through genocide, but through choosing not to breed. I for one have (unknowingly) chosen to join this movement long ago. Personally, I think extinction is a bit severe, but oh well.
The way I see it, though, the driving ideals of the movement are a bit flawed. It is the belief of the movement that the Human species is responsible for essentially "ruining Nature." What it's failing to understand is that "Nature" is larger than the ozone layer and coral reefs. Nature is the sum of all natural physical and metaphyical entities, natural laws, and anything not attributed as "godly."
Thus, Nature encompasses the Universe, and cannot possibly be affected by the insignificance of Humanity. The inevitable supernova of the Sun will unleash far greater destruction upon Earth than measly Humans could do in a billion years! Therefore, it's my proposition that we "screw up" this pathetic planet as much as we can to help the Sun along when it "decides" to blow up!