This gentleman posed some questions to US atheists, looking for feedback for some research he is doing. It is a worthwhile read, and the questions posed are legitimate ones. Read it here. My response follows:
Firstly, I do believe you have a valid point, in that 'new atheism' (a term I don't care for--more on that later) in the states is somewhat more outspoken and strident in the US than in the UK, and for the reasons you describe. Non-theists are forced to be more vocal in the States because we are under a greater assault for their non-belief than our counterparts in the UK. Religious fervor has experienced a tremendous resurgence in recent years in the US, & the rise of 'new atheism' in the US is a response to that.
As to the term 'new atheism,' and what atheism means to me, I agree with Sam Harris: 'atheism' is a word that shouldn't need to exist. We shouldn't have to have a word to describe the lack of belief in a supreme being any more than we'd have a word describing non-belief in astrology or the non-belief that Elvis is alive. In terms of the role of atheism in my life, I don't consider it central to my life, but it is more prominent and present in my thinking and my worldview precisely *because* of the danger that religious belief presents to peace and freedom as it is manifested in the 21st century (and how incompatible the apocalyptic nature of the three Abrahamic religions are with the survival of humanity, given 21st-century technology & weaponry).
My lack of belief in a supreme being would occupy the same tiny, dusty, neglected corner of my mind as my lack of belief in faeries, unicorns, and Elvis being alive, were it not for the significant influence that religious belief has on some of our elected officials--and thus, on public policy.
You asked if there were any atheist Republicans. Yes, there are. They are few and far between (at least publicly--I suspect their numbers are greater in private), but they definitely exist. I was one. I identify as Libertarian now, but I am still very much on the conservative end of the spectrum. I espouse most 'conservative values' as they relate to strong defense, fiscal responsibility, individual freedom & self-reliance.
The Republican party used to be the party of the individual, the party that wanted to keep government out of the way of "the little guy" to the greatest degree possible. Just as the Democratic party has been hijacked by extremists on the left, the Republican party has been hijacked by extremists on the religious right. I firmly believe that the religiously-motivated agenda of social conservatives, which motivates them to crusade against abortion, gay marriage, and a host of other *entirely* personal and private issues, is directly contrary to the central ideal of conservatism--empowering the individual. You can't rail against government intrusion in matters of health care, business regulation, states' rights, and other issues of individual liberty on one hand, while advocating government intrusion into the most private matters of all, like what you do with your body or with whom you have sex. This is a schizophrenic worldview, one that is a constant source of internal friction within the political right in the US, and one that can be entirely lain at the feet of religious belief.
As far as the assertion that religion or religious belief is the cause of ALL violence and strife in the world, I flatly reject that notion as ludicrous, as would the atheists I know. I have never asserted that, and I do not recall that Dr. Dawkins has ever made that assertion either. Religion is not responsible for ALL war, violence, etc, but it is responsible for quite an extraordinary amount, and that is, in my view, undeniable. It is, of course, not ALL religious views that have been responsible for the evils of the world, either.
Divorced from the political considerations with which religious belief and the lack thereof have become so intertwined, I simply believe that religious belief is wholly unnecessary to human life. Religion of any stripe is an attempt to explain the unknown, and make order of the mysterious. We have a tool for that now--it's called science. We are far from unraveling all the mysteries of the universe, but science has, in a relatively short time, given us a far greater and far more reliable knowledge of ourselves and our world than religion ever did. Science offers us a concrete methodology for testing our assertions about the world. Religion offers only the assertions. Even in areas where it doesn't threaten the security of the world, belief in the supernatural is superfluous, restricts our search for REAL answers, and curbs our growth as a species.
In terms of how it has affected me personally, it has not alienated me from family, but I am extremely quiet about it in my work life, as I work for people who are enthusiastically Christian, and my atheism would almost certainly put me at odds with them. I have joined some atheist groups in my newly-adopted hometown, but that is more for social interaction than any kind of activism.
I hope that I have answered your questions, and will be happy to clarify.