Cutting against the grain, I would classify atheism with the left-wing in that atheism as it exists as a mainstream phenomenon fights for overturning traditional ways of thinking about the relationship between man and society. It's true that atheism is not directly political and it is very possible in principle to be a right-wing atheist, but I cannot think of an example of atheism intersecting with politics where the result hasn't been an active effort to push the Overton Window to the left.
This is a good post in reply to a question that's easy for us to dismiss: "there's no *logical* connection between belief in God and beliefs about how to order society, therefore the question is stupid". But I agree a strong case can be made that atheism as a whole movement would tend to the left insofar as it disbelieves in any divinely-ordered hierarchy, and divinely-ordered hierarchy has traditionally been the dominant justification for hierarchy in society. And the atheist who believes in N-1 hierarchies will ceteris paribus be more left wing than the theist who believes in N hierarchies. This is a good reason to believe that atheism will be more of the left.
But as you say, it is contingent ('atheism as it exists'). One could imagine a society some centuries hence which is thoroughly atheistic and justifications of hierarchy are exclusively on some rational economic, or biological, or Nietzschean ground, where then theism as an idea becomes opposed to those existing hierarchies and atheism is an ideological defence of them.
Poll
