Steven Den Beste, a mechanist atheist, writes:
And even among mechanists there's no particular consensus about such things as ethics, because the basic axiom of mechanistic atheism (that the only thing which exists is the material universe and the matter within it, which interacts according to the laws of physics) doesn't provide any kind of guidance in those areas.
Actually, mechanist atheism as defined here, does give guidance about ethics: it states that ethics (and more generally, explanations) do not exist. This comes from the simple premise that ethics are neither matter nor laws of physics.
A much better way to approach existence, is to consider things to exist if they are necessary to explaining reality. This still includes the laws of physics, and all the matter in the "material universe" and still fails to include God or faeries, but this time does include explanations.