This seems to me to be a question of relativist Vs absolutist thinking as applied to meaning. You seem to be suggesting that atheists necessarily take a self defining approach to what constitutes meaning (i.e. a relativist position) and that theists necessarily take an absolutist approach. An approach whereby some external entity is ultimately the objective arbiter of that which is or is not meaningful.
Is that right?
For a religious person, like myself (sometimes), meaning implies an actual purpose or significance in the grand scheme of things. This is a purpose or significance that is defined externally (by some outside agent), and could (if it were true) be objectively verified by other observers.
But isn’t that meaning at root defined by faith and personal belief? In which case it is as internal, personal and as unable to be verified as any atheistic equivalent. Yes there might be significant common ground between those of the same (or comparable) faiths. But any more so than the commonality of meaning that might be cited by atheists of common cultural background?
The main difference between the theist and the atheist in this regard would seem to be the conviction that ones own (or more accurately ones community) sense of meaning should apply to others.
For a non-religious person, like the other (smaller) half of me, meaning implies a feeling or sense of purpose or significance. This is a purpose or significance that is defined internally, and could exist even if no other observers could verify it objectively.
And yet what constitutes meaning for any given person is necessarily influenced by instinctive (i.e. species wide psychological) factors (how many people will cite their children as providing them with some sort of profound meaning?) as well as a complex web of social and cultural factors on top. So atheists are not defining meaning in some sort of internal vacuum. There are significant external influences. These influences are just less strident in imposing conviction than a more theistic approach whereby the community in question actively believes itself to have a more objective basis for imposing it’s sense of meaning onto others.
But, for the Atheist, nothing external is claimed to be the cause of the sense of significance, so there is no equivalent concept in Atheism to what the Theist calls meaning.
I think you are underplaying how much purely internal subjective influence there is on what theists would call meaningful (whatever they believe to the contrary) and also underplaying how much external factors play in determining that which an atheist would consider to be meaningful (whatever they believe to the contrary).
The whole thing is a heady mix of instinct, culture and (if it exists at all) free-will and individual personality. I think this is as true for a theist as it is an atheist. We just ascribe different labels to the causes of our sense of meaning. This in turn promotes different degrees of conviction that ones own sense of meaning is somehow more profound.
But ultimately I think there is little
actual difference beyond conviction that ones own sense of meaning
should apply to others.