Atheism and religions don't belong to any specific side of the political spectrum. There are atheist and religious people from the far left to the far right.
There are many leftist atheists. Most of the marxists are atheists. But I think that the 2000s militant atheism of Sam Harris, Richard Dawkins and Christopher Hitchens are usually supported by people of the center and center-right.
(I am obviously ignoring the ridiculousness of this thread to respond to your post directly, lol...)
You might have a point with Hitchens and his outspoken opinions RE: Bush Era politics, but I don't know about the other two. The most "right wing" thing I have seen Richard Dawkins say is that there are two biological sexes and that is all there is to it ... this is just considered a basic fact by 99.9% of people and does not really speak to ideology. Meanwhile, Sam Harris has openly said that to lie and conceal information if it prevents Donald Trump from being elected is an unambiguous moral good, lol. And he supports a "science-based morality" that would be so far past Marxism's tearing down of Western cultural norms that I don't even know how we could classify it.