FROM wiki (again)<quoted text>
Atheist Jews are no longer ethnoreligious Jews.
They are now simply ethnic Jews.
Why is this so difficult to comprehend for you?
Ethnoreligious communities define their ethnic identity NEITHER exclusively by ancestral heritage NOR simply by religious affiliation, but often through a combination of both-
(a long shared history; a cultural tradition of its own; either a common geographical origin, or descent from a small number of common ancestors; a common language, not necessarily peculiar to the group; a common literature peculiar to the group; a common religion different from that of neighbouring groups; being a minority or being an oppressed or a dominant group within a larger community).
I would add that if the atheistic Jew still have any of those ties within their consciousness that are listed above, they are still "ethinc" Jews. And if they loose those cultural ties, and the religion, simply, they are no longer Jews (and why would they be at that point?).
And if that same former ethnic atheistic Jew, who is now fully assimilated, is reminded that his mom was Jewish, the fact that this fact is now on the table, now makes that person a (ethnic) Jew, at least for the time being.
You are correct - it really isnt that complicated.