I don't presume to speak for those who are atheistic, but how is it "religious" to report an after-death experience, or to suggest that death may not be the end of our existence.
I've never understood atheism to require a belief in the termination of existence at death. Some may believe that way, but I would think it's quite possible to believe that death involves some sort of evolution to another dimension or level of being, not involving a "god," or a "church" or any religious trappings, but simply being the way the universe operates...some law of the conservation of energy or something.
And I think that many who are facing serious illness find comfort in believing that death is not a complete termination of their existence.
I know we have a number of folks on the site who are atheistic, and I certainly have no desire to offend them, but just because this neurosurgeon, or others who have had these near-death experiences speak of them in religious terms, that's their interpretation based on their individiual beliefs. There are other explanations that don't require a belief in a supreme being, angels, heaven, or any of those religious conventions.