While we're talking about the New Atheists, what do they really say? You'd think, from the various denunciations, etc., that they just come out with long, unstructured, uncivil rants against religion. Who would think that the core New Atheist books contain detailed, thoughtful arguments and that they actually make out cases for certain ideas? You may disagree with those ideas, but surely they are worth rational discussion.
At the risk of being reductive, I think the following is a reasonable starting point to identify what they are really on about.
Sam Harris, The End of Faith. What people believe will actually motivate their actions. Therefore, we cannot simply be tolerant of all beliefs. At least some level of pushback against extreme religious beliefs is justified, and moderate religious people are not assisting with this.
Richard Dawkins, The God Delusion. Orthodox or popular theism can be seen as a persistent false belief, one that survives in the absence of evidence and even against our best evidence of how the universe works. Furthermore, it causes actual, identifiable harms.
Daniel Dennett, Breaking the Spell. We ought to devote a lot more time and energy to the study of religion as a natural phenomenon. This will be more useful than the current deference to religion and assumption that it is at least socially valuable (if not actually true).
Christopher Hitchens, God Is Not Great. The big problem with religion, especially with Christianity, is not so much that it's false as that it comprehensively denigrates human nature and valuable human experience. In that sense, it "poisons everything".
Doubtless all four (well all three, plus Hitchens before his untimely death) would tend to support the main ideas of the others. But they have different specific concerns and different emphases, and they do put actual arguments for their positions. Importantly, while they don't mince words they do remain within broadly accepted standards for civility.
They deserve to be engaged in detail, with appropriate arguments, qualified agreement where that is appropriate, and so on. Instead, the response is often merely an attempt to demonise them and thus try to neutralise them as contributors to debate in the public sphere. That's not good enough.