Religion comes from Re- (Re) -ligion (union), which usually ends up meaning [i]Reunion of people[/i]. There can be religion without God, an Atheists belong to a religion that [b]doesn't[/b] believe in God, period.
People who justify their actions upon "God's will" are wrong. Theism is a lie too, as religion is supposed to be based on mutual support to achieve spiritual freedom, not fanatical worship over a God, used to manipulate weaker minds into their cause.
Now, deism is a different thing, it [i]is[/i] the way religion was always intended to be, an interpretation to live life based on teachings, that help humanity to achieve plenitude.
So in the end, theism is just a way to justify inhuman actions (looking at you extreme muslims), atheism [b]is a religion[/b], and deism is the way to live religion as a reunion of people with the same beliefs.
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I see where you're going but I wouldn't say atheism is a religion. I wouldn't even say theism is a religion. A religion is a system of beliefs centered around the worship of God or gods, whereas terms like theism, agnosticism, and atheism are more about what one believes regarding whether or not God or gods exists. Since religion involves the worship of God, this rules out agnosticism and atheism. The reason being that by definition, an agnostic is a person who does not believe God exists and does not believe God does not exist; they take the neutral position of 'I don't know.' And by definition, an atheist is a person who believes God does not exist; in other words, they do not believe that God exists, so they of course don't worship God. A theist is simply a person who believes that God or gods exist, but does this make theism a religion? No, because a theist may simply believe in a higher power or a creator (i.e., God) but have no clear concept of what that higher power is and may not worship it - God - in any way, shape, or form.