So, the first problem you're going to have is people (including you!) throwing around terms without agreed on definitions. To wit:
"It not uncommon to see religious people arguing that without the moral center of a religious text, true ethics are impossible."
It's helpful to separate "morals" from "ethics", and this actually simplifies the question. Let us say that "moraliy" (from "mores") refers to the customs of a people. Ethics (which at its root, refers to the nature of a thing) is a measuring of actual good vs. bad (and we'll smoothly elide what "good" and "bad" are to keep this short :-)) in a particular situation.
Almost anyone can follow morals. Atheists do it all the time. Criminals have a hard time with it, that's why they're criminals. But the thing about morals is that they're based in the past.
For a contrived, simplistic example, let's say Chaim eats pork and dies of trichinosis, and so our people evolve a rule of "don't eat pork". But 5,000 years later, pork is pretty good. Chaim's people still don't eat it, because it is forbidden. A lot of people will say that's silly, but if you look at the root of the word "religion" you find "to bind", and our behaviors and proscriptions of behaviors are what bind us together.
So, even while the health issue—the root of the moral—may be gone, it still may be immoral to eat pork, as it weakens the bonds that holds a people together. I've known a lot of atheists who adhered to a moral code precisely because they saw the value of that bond.
But what about the question of good and bad, right and wrong—ethics, for the purpose of this response. Ethics and morals can clash. If we continue our contrived example, and Chaim is starving, and he must eat pork or die, the ethical response is for Chaim to eat it. Depending on the group he belongs to, this may or may not be viewed as something that requires atonement, and some groups might kill him for his transgression (at least theoretically).
Atheists* can do this as well, i.e., they're capable of weighting the rightness and wrongness of a situation.
Atheism, however, shares with religion the trait of being used as an excuse for bad behavior. Why, it's almost as if Man contrives to justify doing bad things, regardless of whether he uses Gnosticism or Marxism as an excuse. Strident atheists may become so because, say, drinking and fornication is prohibited and they love to drink and f***.
Too, religious splinter groups often emerge as a way to allow a certain behavior prohibited in the religion. Like: divorce, having multiple wives, theft (call it "from each according to his ability"). But also, on the flip side, things like allowing music, dancing, bathing and so on.
Whether religious or atheist, it's also true that people looking to change things are the sorts who have no respect for Chesterton's fence. A really good example of this can be seen, routinely, in the area of sex, where science has drastically reduced the threat of disease or unwanted reproduction, yet there still seem to be noticeable, statistically observable effects regarding not just promiscuity but anything less than severe monogamy. (Nobody wants to hear it but if you want to be married for life, you should be a virgin and marry a virgin.) But the big jokes today are those who counsel restraint.
- To really wrap this up, I need to point out that atheists have badly misnamed themselves. They are, more accurately, materialists. An atheist merely doesn't believe in God. Many Buddhists, with a strong belief in the spiritual world, are atheists (as Buddha himself did not claim to be divine). But most modern atheists are inclined to regard any spiritual thing as bunk.
This creates a genuine problem in terms of evaluating good vs. bad: If everything is matter, then literally nothing matters. There is no "good" and "bad" without someone to say "this is good" and "this is bad".
Someone said above that social stability requires morals, but it is not possible to explain why that's important without evaluation, and evaluation requires an observer. If Joe kills Bob or Joe puts out a fire, what's the difference? On what basis do you judge "life" (which must ultimately be a mere chemical reaction) over other phenomena.
And, to boot, who are YOU? The momentary delusion of consciousness created by electrical impulses in a brain? Why am I even trying to communicate with you? =)
But, really, this is something that materialists just glide over. You can see it in this recent popular thing about Star Trek transporters (https://www.youtube.com/watch?v=nQHBAdShgYI). He has to dismiss the ghost, but then comes up with the concept of "the conscious brain". This is the sort of magic materialists fall back on to justify being good and moral—something we can all be grateful for, and which suggests, perhaps, that Man, regardless of his moral and ethical structure, has a drive to be good. Because if we are nothing but arrangements of particles, it really doesn't matter if we're killed every time we step into the transporter.
Anyway, as religious people point out, it is totally possible for an "atheist" to discard all morals and ethics, and do whatever he thinks his best for him that he can escape punishment in attaining. But these people are called sociopaths, and they're perfectly capable of pretending to be religious.