Religion probably requires a belief in the qualities of ideas guarded by an individual and usually guarded by a community, as well. So a “non-theist religion” probably cannot be, because there is no idea to “believe in,” or guard against deterioration of its value.
Atheism is not a religion, just as theism is not a religion. Theism is a category of ontology - what exists. Theism is an ontological doctrine that prescribes the existence of a supernatural dimension of human experience. Atheism is not the opposite of theism as the prefix “a-” suggests, because atheism cannot be an ontology - humanism is the ontological doctrine that prescribes that humans define reality.
Atheism is a political doctrine that opposes theist doctrine for use in public policy.
When atheists defend the definitions suggesting anything like “lack of belief . . ,” and support it with the etymology of it having been defined in ancient times before even the word “theism” was documented, they are making the mistake that atheists tend to accuse theists of committing - reliance on poorly supported legends.
Back in those days there was no demarcation between religion and politics as we try to do so in the contemporary.