Except no one reasonable has ever changed a core value from monday to tuesday, including atheist. Religion is not the only source of internalized morality that is consistent over a period of time.
I'm not sure how to make it more clear, but I'll try.
An atheist's value system is internal. It can not be evaluated by others, because it is not written, not discussed in groups, not consistent amongst a group. There's no reason for it to not change from Monday to Tuesday, because there is no established, taught, consistent, written, known, reviewable, understood, socialized, shared core value system. From LDS to Roman Catholic, there are consistent Christian values. People understand that there are minor differences (whether you may dance or not, the level of PDA, little #### like that) amongst Christian denominations, but they're all Christian. Christian's get Jews and vice versa. Pretty major disagreement on whether or not the Christ has come, but the base value system is consistently understood because people can read each other's books and follow the logic of why one believes what they do. Muslims have a grossly different view of things than Christians or Jews, but they have a book and teach on at least a weekly basis about their value system as well.
Atheists have nothing - that's kind of the definition. They have whatever they think that minute. I can't review what atheists think, because there is no such thing as an atheist's guide to morals, to values. There is no such thing as an atheist's bible - again, part of the definition. Whatever an atheist believes that minute is that atheist's core value system. If a major event occurs in an atheist's life, that can instantly, drastically change that atheist's point of view, their core values. A Christian, for example of a religious person, will (as Pres. Obama famously phrased it) cling to their Bible to help them through with a consistent set of core values unchanged. Some religious people have their faith shaken by significant life events, but either become atheists and lose their core value system, or become strengthened in their faith and are stronger religious people.
This is not a slam on atheists or a reason for religious people to claim any kind of superiority. It's simply in the definitions. Yes, religious people break their own rules (sin), and that's a bad thing. Atheists can just change their rules at will, and the break becomes the new rule.
I've never claimed religion as the only source of internalized morality that is consistent. Certainly an atheist can choose to maintain consistent core values. They each, individually, on a moment by moment basis, make that choice. A religious person is given a set of morals, and over generations how those morals are viewed might evolve some. A non-religious person decides for themselves what their set of morals are, and over the course of an afternoon their morals might evolve some, because the only thing they have to benchmark their value system against is their own thoughts.
Again, most American atheists actually have a Judeo-Christian ethic system, because that is the ethic system of the society in which they were raised, and thus what they have internalized as "right" and "wrong". That doesn't change the fact that their view is malleable at will, with no written, consistent standard by which to judge their internalized-understanding of what is "right" and "wrong". It can be consistent as a granite statue, or as consistent as leaf in a hurricane - it's their choice. A religious person's values have a granite statue of a book to follow. Granite statues change, but slowly over time. Leafs get blown around in hurricanes pretty easily.
Don't take offense, because absolutely none is intended here. It's really just a part of the definition of each. Neither side can establish superiority, because to have superiority one must have a consistent standard by which to judge better or worse. Atheists and religious folk do not have consistent standards amongst themselves, so neither can reasonably claim superiority over the other. My way of thinking is superior to my way of thinking, your way of thinking is superior to your way of thinking, but there's no conversion chart, no equation by which my way of thinking can be compared to yours, or to the Muslim's, or the Jew's, or those who choose to follow the FSM. We're just different, and that's ok.
