The New Atheist project is to criticize religion. We pursue this project by a variety of means: from the driest philosophical analysis (e.g. me) to polemics to mockery gentle (e.g. Jesus and Mo) and savage (e.g. Charlie Hebdo). We have our flaw, but only a minority* of New Atheists support geopolitical violence (and that's because most New Atheists are also citizens of imperialist nations, and Western imperialism is not a project initiated by New Atheists), and I literally know of zero New Atheists who condone, much less advocate, personal violence. Regardless of his motivations, regardless even of his opinion of religion, Craig Hicks' murders are absolutely infantile. Our project is not about our enmity with religious people; our project is our criticism of a way of thinking. We want people to be happier, not dead, and we believe religion makes most people unhappier than they could be. And, unlike for example, Black people, atheists are not generally subject to unjust state violence (and many benefit from unjust white, male, class, heteronormative, and cis-gendered privilege); we have no particular need of armed self-defense.
*That's my sense, without the rigorous statistical analysis I don't have the resources to perform.
There are, I will repeat, right-wing, American exceptionalist New Atheists, e.g. Sam Harris, Christopher Hitchens, and Ayaan Hirsi Ali, but their advocacy for Western imperialism is as much politically motivated as religiously, and they are, with no small hypocrisy, allied with an explicitly Christian government. But if you look at what we actually say, you will find neither passive acceptance nor active advocacy for personal violence against religious people. The worst I think you can find is, as PZ Myers argues, a lack of attention specifically to creating a positive ethical system.* But you will find no New Atheists listing Muslims to kill, you will find no New Atheists glorifying cowardly criminals such as Hicks, you will find no New Atheists saying, "The only good Muslim is a dead Muslim." And if you do find such a site, let me know: I will lead the charge against them, and not just exclude them from the New Atheist community, but make them the object of public ridicule. (And if my charge is unsuccessful, then I would leave the New Atheist community instantly.)
*I don't particularly agree with Myers. Almost all New Atheists take a level of ethical functioning for granted, a level that obviously excludes Hicks, and it's boring to talk about things we all agree about. It's much more interesting to talk about our general ethical lapses, e.g. the rampant sexism and only-slightly-less-rampant racism within the atheist community.
Our project is to criticize religion, to delegitimize religion as political and social power. If you want to go to church on Sunday, that's your own business, but if you put your collar on backwards, study the mythology of early Iron Age slaveowning patriarchal goat... herders, you still have zero special privilege to set the moral, ethical, or political agenda.
Religious people despise our project, and they want us to just shut the fuck up. All religious people want to preserve religious privilege in general, and then argue — or fight — about which religion is better. Even the Infamous Brad would rather excuse the misogyny, homophobia, anti-science propaganda, right-wing authoritarianism, and scriptural support for violence in Islam than admit his own religion is at best a hobby and at worst a delusion.
If the primary cause of religious bigotry, discrimination, oppression, and violence were New Atheists' criticism of all religion, then there might be some case for asking us to rethink our position. But the real primary cause of religious bigotry, discrimination, oppression, and violence is, of course, religion itself. You say that religion had nothing whatsoever to do with the Charlie Hebdo murders? That relgion had nothing whatsoever to do with murders of David Gunn, John Britton, James Barrett, Shannon Lowney, Lee Ann Nichols, Robert Sanderson, Barnett Slepian, and George Tiller? That no one ever religiously justifies the abuse of children? That religion had nothing to do with the Indian Partition and between 200,000 and 1,000,000 deaths? Fair enough; even the New Atheists will admit that there are a lot of political and non-religious cultural reasons going on there. But then you say it's ridiculously obtuse denialism that New Atheists might look for other reasons for Hicks' murders?
I seem to recall something about beams and motes in the Bible.
You religious people want to slaughter each other over your gods. Not all of you, and, lately not even most of you, but a lot of you: even per capita a lot more religious people want to slaughter other religious people than New Atheists want to slaughter anyone. (Sometimes just because of different religions; more often using religion to justify the slaughter.) And most of you no longer want to slaughter each other in no small part because of us, the atheists, secularists and some religious people, all of whom dared subject religious beliefs to rational scrutiny, and to condemn the stupidity and brutality of those beliefs on secular, humanistic grounds.
We're having none of that. We will generally condemn Hicks, he is no longer "one of us" in any sense. He is no longer a New Atheist because we define New Atheism to exclude infantile personal violence: it's our group, and we can define ourselves as we please. Anyone who praises Hicks, anyone who advocates what Hicks did, is right the fuck out. And not just out of our community: we will do what we can to humiliate, delegitimize, and, for such as Hicks, advocate state power to punish, those people in public society.
But we will not shut up. We will not stop criticizing religion. We will not stop pointing out the stupidity, cruelty, and brutality of religion, and we will not stop saying that what you think God does or does not want, good or bad, has nothing whatsoever to do with how reasonable, caring, loving, empathetic and sympathetic human beings behave towards each other.