Internal revolutions, i.e. schisms, are key in my understanding too. I suspect that all the wars of the Reformation had a lot to do with the re-invention of the concept of religious toleration and its eventual spread across Europe. But perhaps even without soaking a continent in blood, schism can do its work. Exposure to a variety of religions seems likely to make people skeptical of enthroning any one of them.

Thus, atheism is only marginally relevant to freedom from religious oppression. The real key is alternate religions. If you would free people, underwrite the books or broadcasts by the next Erasmus or Luther or Rumi.