If the definition of "atheist" has to do with not believing in God, it has nothing to do with not being a part of a group. Atheists can be part of religious groups and many are.
Atheists are atheists because they don't believe in any gods. If you say anything more than that, then you are misleading yourself by what you mean by "atheist".
The word atheism comes to us from the Greek through the French and means "a" without + "theos" god=with god.
It really had nothing whatever to do with "belief" until very, very recently...the Internet age, in fact.
I agree that most atheists these days (particularly Internet atheists) base their use of "atheist" to describe their position on "a lack of 'belief' in a god", but I think you do an injustice to the word by defining that part of it so restrictedly.
There is a mistaken assertion at times given that atheism came from "a" without + "theism" a belief in god = without a belief in god. But "atheism" came into the English language before theism...so a case can be made that the latter derived from the former, but not the former from the latter.