What are the similarities and differences between atheist arguments and anarchistic arguments?

Atheism generally approaches arguments about the existence of deities with skepticism, ranging from extreme to rational. In some cases, the idea of the necessity of a higher moral authority is eschewed in favor of reliance on humankind to determine its own morality. Much of the vocal concern is aimed at the argument that religious institutions and how religion has been used as, as some say, the most destructive force humanity has seen.

Anarchy approaches the idea of the state with skepticism. The argument is often based on the idea that the formal mechanism of the state is unnecessary for people to determine a way to live with one another based on natural principles of fairness, and is destructive to liberty. The most vocal concern is directed at the fact that the state is the most destructive force, producing more violence than anything else.

One famous argument I’ll paraphrase is that democracy is the worst form of government besides all the other forms of government there have ever been. I would like to know how people think atheist and anarchist arguments play against each other, how the rhetoric is similar, and how they can inform each other – and how if one is an invalid conception, how that validates or potentially invalidates the other.

Thanks!