Everyone is religious and everyone has a religion because religion is central to human existence. So, atheists have a religion of some sort, even if they deny it.
For some religious theists, their religion and religious beliefs are so important to them that they can't imagine anyone being without a religion of some sort. For such people, religion occupies such a fundamental and necessary aspect of how they live that they insist the same must be true of everyone. Thus everyone must have a religion of some sort and it's impossible for anyone to live without one. This includes irreligious atheists who insist that they really don't have any religion.
Many people use the term homo religious to refer to the concept that human beings are naturally and innately religious. This often occurs in the context of claiming that every person naturally seeks God or at least some "higher power" to guide them in life. Claims like this essentially assert the truth of disputed religious propositions (Begging the Question fallacy), denying that atheists' self-reported absence of any such feelings can be true or genuine. People making claims like this are also saying that feelings or inclinations which are popular must necessarily be true of everyone (argumentum ad populum fallacy).
According to this argument, those who insist they are different and have no religious feelings, inclinations, or beliefs, are lying, don't really understand themselves, or if for some reason are correct then they must be disturbed because their position is "unnatural." If by some chance they accept as true the claim that they really do have a religion, then all of their critiques of religion and theism can be said to apply to themselves as well. Whatever the case, it's safe to dismiss them as having anything useful, interesting, or relevant to say on religious matters.
Another popular tactic for promoting this myth is to redefine the concept of "religion" with very broad and ambiguous strokes, calling it a person's "ultimate concern" or "whatever is most important in your life." There is also very often a redefinition of "worship," making it mean something as trivial as "intense attention." Once the redefinition of all the key terms is completed, it's possible to insist that everyone "worships" something because everyone pays "intense attention" to something, and if this is what is "most important" in their lives, then it must be their "religion."
With categories so ambiguous, it doesn't take much creativity to argue that a person is religious about something if one is determined to do so. Such tactics are merely an example grasping for straws, though. Just because you can identify the one most important thing in someone's life doesn't mean they have constructed a religion around it.
This is not to say that atheists live such bland lives that nothing is important or relevant to them. Quite the contrary, atheists can live very full and interesting lives, and atheists do generally regard something(s) as important to them. Indeed, an atheist might even go as far as to revere certain political figures, artists, works of art, ideas, etc.
None of this, however, is the same as having a religion when used in the traditional religious sense. That is why the above claim also commits the Fallacy of Equivocation: it starts out using the term "religion" in the standard manner and ends up using it in a very different way. To be a valid argument, it would have to use the terms in exactly the manner all the way through.
Also, if we keep in mind the fact that theists hold some things in equal regard as atheists, what happens is that both atheists and theists even Christians end up having multiple religions. Is that what the above myth really intends?
Particularly bizarre about this argument is how it does a grave injustice to genuine religions. If a person says that my "religion" is atheism because I spend a lot of time writing about it, just like they spend a lot of time reading the Bible or going to church, they are not only misrepresenting me but they are also denigrating themselves, their religion and their god. Religions like Christianity, Judaism, and Islam are complex systems of beliefs, traditions, attitudes, morals, stories, behaviors, and more. An atheist's concern about the environment, activism in politics, or writing about philosophy isn't anything like those systems and simply cannot be compared to them without significantly misrepresenting one, the other, or both.
It is a sign of significant desperation when someone deliberately undercuts their own religious beliefs and commitment in order to score false rhetorical points in an argument. Because the main conclusion that can be derived from this myth is the ability to dismiss and ignore what atheists have to say, however, perhaps the loss is considered well worth the final gain: the marginalization of critics and their criticisms.