I often hear from Theists (seemingly recognizing the flaws in religious thinking) saying that Atheism is a religion.

I would like very much to discuss that.

From a perspective most things conclude as being subjective, then transmogrify accordingly; but their roots remain intact. So, if you look in a dictionary for the word religion you find the most common use in the culture you live in. Maybe the etymology is given, which is where you find the root and how that root grew into the common use. An encyclopedia may give you some insight on the perception, and with all of that you can break it down and simplify it.

Religion is a strict adherence to a set of principles/belief and a specific methodology of repetition. Everyone is religious. Every religion i.e. everyone is flawed.

Here is how religion works. A belief, philosophy or subjective fact dependent upon faith is proposed and then propagated to the masses. If those are widely accepted they become useful tools for social and political means. Typically the original teachings of the religion are transmogrified in the process - often for the political means itself - which, through a gradual and insidious process of a cultural, social and traditional influence, becomes the paradigm. You see this in the Emperor Constantine the Great's politicization of Christianity and the Nicaean creed. You see it with the Emperor Wu Ti's promotion of Confucianism and interest in Taoism. Shintoism was named as such due to a need for a distinction between ancient Japanese cultural ritualistic festivals during the planting and harvesting seasons and the newly introduced Buddhism from India. It was then incorporated into the mythological instruction of Japanese youth through the legends of the Nihongi and Kojiki by the Royal family.