I agree that atheism by definition is inherently a religiously based position; that's why I refer to myself as non-religious rather than something like atheist.
I'd say it may even be a word that was invented by theistic vanguards as a means of control, via our means of communication, over both folks who are their religious followers and those who aren't their religious followers; it sort of creates this false dichotomy about where people stand religiously, and it seems effective.
The false dichotomy is either you're a religious follower, or you're not a religious follower yet because you haven't been persuaded; for example, you do believe in God (a supernatural being who created the universe and is going to judge you after you die to determine whether your soul gets to go to heaven or hell), or you don't believe in God (yet), because you haven't been persuaded so far, and you're open to being persuaded.
In reality, there's more than that; there are those who are not interested at a fundamental level in believing anything religious or supernatural. They're not religious, or I suppose one could say that the have religious apathy - they don't care to the point that they're not interested in exploring religious belief, or far more likely it's that they are very familiar with religious material - the doctrine, dogma, rituals, etc. and see them as useless and pointless.
I was raised by religious parents, and am familiar with the doctrine, dogma, rituals, etc. For a while I was a believer, but eventually I decided to drop it as I don't see it as useful, beneficial, or practical for anything. I don't see myself as going from theist to atheist, but rather as having gone from being religious to non-religious.
Some atheists seem to take the approach that they're open to persuasion, but in practice I don't think that's what they really want to do; it could be that their goal is to try to break people who are religious believers and get them to stop believing, but from what I can tell they're usually don't have much of any success.
Some individuals who claim to be atheists might actually be religious believers or religious vanguard types pretending to be non-believers or atheists, to try to first get some atheist or non-religious individuals to become their followers in the hopes of eventually converting them to their religious beliefs; they're playing a con game.
I think many individuals who identify as atheist do so because they're simply not interested in being religious, but haven't put enough effort into making the distinction between someone who has fallen into that religious trap that the religious theists have lured them into, and realizing that "atheist" may not be the correct term; they should, instead, just say that they're not religious; this way it won't attract folks who are religious to them to try to convert them to their religion.