Atheism is the conceptual position that God/gods don't exist.
I'ld rephrase that as "the practical position that gods don't exist" and I might get on board with it.
For all practical intents and purposes, yes, I live my life
as if gods don't exist. For the simple reason that I don't believe they do exist. Not because I actively believe they don't exist. There's a difference.
Let's use an analogy of a mythical beast we can both agree is mythical, that you don't believe in either.
Let's say that there is the claim that an undetectable dragon is circling the highway, waiting for the right blood to come along to feed itself. Let's say the claim includes that the only way to be certain that this dragon won't eat you, is by wrapping yourself in tinfoil. Because then the dragon can't smell you or something and you appear invisible to it or whatever.
We can say that we don't believe this claim. Can we demonstrate it to be false; disprove it? Absolutely not. We can never prove this undetectable dragon isn't real. We simply don't believe the claim that he is real. He could be real. We can't show he's not. We simply have no reason to believe it to be real...
Now suppose we need to drive over this highway. So for all
practical intents and purposes, we now have a choice to make. Do we drive over this highway wrapped in tinfoil or not?
If the answer is "without tin foil wrapping", then that means that for all practical intents and purposes, we assume this dragon isn't real and that we aren't risking anything by driving the highway without being wrapped in tin foil.
As an atheist, I view gods - and by extension the supernatural in general - exactly in this way.
I have no reason to believe it's real.
I can't disprove it.
For all practical intents and purposes, I live my life as if it isn't real. Really, because I have no other choice. The alternative would be to go through life assuming is real without actually believing it to be real.
Also, to be logically consistent, I'ld also have to go through life assuming EVERY unfalsifiable claim is correct. And unfalsifiable claims are infinite in number. And mutually exclusive.
So yeah, that wouldn't work.