1) We atheists are not doctrinaire; we follow the evidence. That is a stark and significantly profound difference between atheism and any religion, whether it's a new, utopian one as hypothetically posited in your comment, or not. There is no such thing as one religion being more rational or efficacious than others. Mormons, Baptists, Catholics, Jews, Muslims, Hindus, etc., etc., ad infinitum - they all think all the others are crazy, if not evil - a judgment about which they are all equally correct, because ALL religions are based on supernatural musings, and superstitious fears, not on empirical or even logical evidence. A good one-word descriptor applicable to ALL religions is "cowardice." They are all cowardly attempts to assuage the paralyzing fear of death through the invention of existential fairy tales that are patently preposterous - "Santa Claus" for adults. We atheists, on the other hand, bravely take what nature presents, try to improve upon it, and live with it to the best of our ability and with our most humanistic of intentions.
2) We should continue to see the truth and share our knowledge and reason based on science and rational inquiry whenever and wherever the opportunity arises, as I am presently doing. I also search the internet for religious sites that allow outsiders (i.e., atheists) to post commentary and opinions; but they are hard to find, because religionists try to erect a barrier between what they WANT to believe and what contrary evidence might intrude. I certainly have never found a website that invites opposing views, as this one does.
3) We should apply the "New Atheist" stratagem whenever and wherever possible. It's not a new "definition," as you state, though. Atheism is, has always been, and will always be simply a LACK of belief in theistic explanations of the natural world. Hey, we were BORN that way. Our brains seek logic; religion rejects it. What has changed is the willingness of some in the atheist community - scientists in particular - to come out of the closet, say what they believe, and support it with their knowledge, training, and eloquence. Bertrand Russell was the first to do it. Carl Sagan followed in his footsteps. And both were roundly castigated for it in the religious community. Dawkins, Dennett, Harris, Hitchens, and others are following in Sagan's footsteps and moving beyond. Even Stephen Hawking has been uncharacteristically edging towards stridency regarding his anti-religious views of late, which is a very good sign, especially since it's beginning to look like he may live forever. Believe me: when he very publicly proclaimed his belief that God was not necessary to explain the universe, a lot of people on both sides of the issue sat up and took notice. Yes, we absolutely should adopt the "new atheist" strategic paradigm.
Explain myself? I hope I did. What is more interesting to me is to explain YOU. I was immediately suspicious when you began your second paragraph with the phrase "atheism theory." That sounds suspiciously like something that came directly out of the little hole-in-the-wall Discovery Institute office in Seattle. I apologize if I'm misinterpreting your intention. If you, yourself, are an atheist, I would suggest you use the word "paradigm," hereafter, rather than "theory."
For the record, atheism is not a "theory." We don't theorize anything affirmatively. We simply admit that we, unlike benighted religionists, DON'T know everything. We are hoping to learn more about as many things as possible. But we cannot accept the notion that the answers can be found in bronze age mythological superstitions that are 100% unsupported by anything resembling "evidence," either empirical or philosophical; or by some black-jacketed compilation of selected contradictory and repeatedly reinterpreted, absurd ramblings of quasi-prophetic, middle east sheepherders, especially since much of it is extremely hateful and inhumane, to say the least.
One more thing: another suspicious phrase you used was "Like us they seek to abolish every belief (or non belief) that is not theirs." The "New Atheists" are not out to abolish anyone's belief. We are out to prevent those beliefs from preventing the progress of society. Religion, by its very nature, is anti-science. Anti-science, in turn, is dangerous - potentially devastating - to society. Religionists who seek to replace science in the classroom with superstition; who wish to supplant evolution with "intelligent design;" who believe God opposes sex education, hates homosexuals, and approves of the assassination of abortion-providing doctors, are planting the seeds of ignorance that will ultimately bring down the United States as a bastion of democracy. Religion, by its very nature, is anti-democratic, as the Calvinistic Puritans were proudly fond of proclaiming ("People don't rule the world, God does.") It's this that the New Atheists are uniting to fight against, not individual beliefs. Richard Dawkins couldn't care less what someone's personal beliefs may be, as long as they don't threaten rational, progressive inquiry from continuing, as it has for the past 400 years, to improve the lives of the citizens of the world. So he goes out and entertainingly educates audiences worldwide about how evolution works, not only with his many brilliant books, but with numerous personal appearances. HE, indeed, is a "New Atheist," in that he wants to spread knowledge to counter ignorance.
This is the party line, so to speak, but there are many followers who take a much more radical stance and it is never treated with disapproval by the New Atheist community.
Not following the evidence
Painting the mass murder of religious people in a positive light
Wanting to abolish peoples beliefs
Associating religious belief and mental illness
Look, this is the same old tired argument that Christians use. This is what a Christian is according to how they ideologically see themselves ""They dwell in their own countries simply as sojourners.... They are in the flesh, but they do not live after the flesh. They pass their days on earth, but they are citizens of heaven. They obey the prescribed laws, and at the same time, they surpass the laws by their lives. They love all men but are persecuted by all. They are unknown and condemned. They are put to death, but [will be] restored to life. They are poor, yet they make many rich. They possess few things; yet, they abound in all. They are dishonored, but in their very dishonor are glorified.... And those who hate them are unable to give any reason for their hatred."
-The Letter to Diognetus
In both cases, they misrepresent what generally occurs.
I'm still waiting for an actual example. A few of those things you list were disapproved of within this very thread. Not all atheists "follow the evidence", which I pointed out earlier in this thread. I have never seen approval of mass murder, tacitly or otherwise, by the atheist community at large. Abolishment of beliefs can be taken a number of ways as I have already pointed out earlier and it isn't always a bad thing (think abolishing the belief in a flat Earth through education). And the association of religious beleif with mental illness is a claim I rarely see aside from a few radical voices that I'm happy to disagree with and repudiate. The closest thing I have seen to that claim is that religion can help hide mental illnessnes and I find that argument to be compelling.
I fail to see how any of these things could be used as an indictment of the so-called "New Atheist" community.
Well, it's not about belief but about what's most rational, right? There's a difference between a belief which is JUST a belief with nothing behind it and a belief supported by evidence or the absence of evidence (like the absence of evidence for Jehovah, for example).