I like cmadler's name for it. Apatheism. That sounds pretty darned close. And, technically, you're not wrong. Whether a God exists or not won't really change my stance on life, nor will it change how I interact with people. I do believe in one, but I don't really see God to be involved in the lives of its creations anyway, so it really doesn't matter if God is there or not. Goodness is meant to be done personally, out of kindness for others, or at least for the good, fuzzy feeling you get when you do something for others. I don't need a God to tell me that, and I don't need God to help me with anything in my life. I was made with strength to do things myself.

The basis of your question is not logical. If you take "belief" out of God religions, you have nothing because that belief is baseless. Atheism is not a belief because there is no baseless belief to take away from it; atheism is a lack of belief. Now, if there was proof of God, then you would have a belief to take away from the stubborn atheist who still refuses to acknowledge this proof. But, this is not the case.

The best term I've heard for what you're describing (the existence of a god is irrelevant) is "apatheism"...it's the "I don't know, and I don't care" 'ism'.

There is plenty of proof that there is no God, at least not in the sense that the world's religions convey IT. One only has to look at all of the different interpretations of the Gods to know that they disprove each other while sharing some of the same root myths. But beyond that, the burden of proof is on the believer. We do not pretend to know if their is a "God" we just know the bullshit they speak is exactly that, bullshit.

Your definition of atheism is slightly off.
Atheism isn't a belief, it's a lack of belief in a god(s). The burden of proof is on believers because they are making a positive claim.

The closest thing I can think of for your question is ignosticism.
The philosophical position that existence of God is meaningless because the term "god" has no unambiguous definition. Ignosticism requires a good, non-controversial definition of god before arguing on its existence.

Even if the god of the bible showed itself in front of me right now, I would acknowledge it's existence but I would never worship the son of a bitch. I believe Matt Dillahunty said that.

secular i think is the word

Buddy you just stumbled onto the point of it. You're just a little off. Atheism isn't belief that there is nothing. Atheism is not believing in anything. Not believing. Belief in my mind is delusion on purpose.

That is a life of drifting in a random, meaningless manner.