One word to describe what you and all other atheists are, rather than what we are not? That's a toughie, Andrew. Why should we necessarily have anything in common other than our rejection of religious explanations of the universe?
Mao and Stalin almost certainly were atheists, and Mugabe probably is one. I hope I don't share too much in common with them.
The British Humanist Society is still around if you're looking for companionship and a label. Possibly the Rationalist Society too (if I remember its name correctly).
My only affiliations are with the American based National Center for Science and Education (NCSE) which those of you who are familiar with Dr. Eugenie Scott will have heard of. But NCSE's membership is not exclusively atheist: many scientists are Christians and Jews.
While I will almost certainly agree with most of the atheists who post on AB on issues like faith schools and such like I'm sure that I will have views on a whole range of issues, political, economic and moral which differ from your and other atheists'.