In general, I believe what we know about human psychology runs contrary to the New Atheist approach and strategy. However, I do my best to follow the data, and here's a study that suggest at least one aspect of their approach may work. The tactic finding support here is not necessarily being confrontational--that would tend to prompt negative emotional reactions, and thus defensiveness and inflexibility towards New Atheist arguments--but rather, making it more widely known that you're actually there--as "out" atheists try to do:
Although prejudice is typically positively related to relative outgroup size, four studies found converging evidence that perceived atheist prevalence reduces anti-atheist prejudice. Study 1 demonstrated that anti-atheist prejudice among religious believers is reduced in countries in which atheists are especially prevalent. Study 2 demonstrated that perceived atheist prevalence is negatively associated with anti-atheist prejudice. Study 3 demonstrated a causal relationship: Reminders of atheist prevalence reduced explicit distrust of atheists. These results appeared distinct from intergroup contact effects. Study 4 demonstrated that prevalence information decreased implicit atheist distrust. The latter two experiments provide the first evidence that mere prevalence information can reduce prejudice against any outgroup. These findings offer insights about anti-atheist prejudice, a poorly understood phenomenon. Furthermore, they suggest both novel directions for future prejudice research and potential interventions that could reduce a variety of prejudices.
Full study here.