You should be clearer on what you mean by "religion," though. You're assuming the loose, Durkheimian or Tillichian sense which is about "unifying values," as in whatever culturally binds a society. But atheism isn't opposed to religion in that sociological sense since "religion" there is synonymous with "culture." Atheists are opposed to theism. It's "a-theism," not "a-religionism."

There are certainly "integrating principles" and institutions that hold together secular societies: liberty, money, art, business, consumerism, progress, technology, knowledge, etc. You can critique those values, and all societies likely have their upsides and downsides. But there are in fact secular cultures that have replaced Christendom.