My biggest issue with the new atheists is the high level of philosophical illiteracy among them. They often don't understand the problems a philosopher might have with their underpinning everything they accept with pretty much nothing. They also don't tend to appreciate how serious things like meaning actually are.
It wouldn't be too uncommon to far a New Atheist to express views like: "OMG you believe something which isn't true. You need to believe in delusional fairy tales because you can't face the truth. Do you even science bro?"
Many also repeat inane, specious memes like:
Now an old atheist, Nietzsche said:
The greatest recent event - that 'God is dead'; that the belief in the Christian God has become unbelievable - is already starting to cast its first shadow over Europe... Even less may one suppose many to know at all what this event really means - and, now that this faith has been undermined, how much must collapse because it was built on this faith, leaned on it, had grown into it - for example, our entire European morality. The Gay Science
Many New Atheists fail to realise the degree to which contemporary society has been shaped by religion, and that rejecting it ultimately this destroys the foundations on which existing morality is built.
This leads to an attempt to recast such ideas in a secular context, the thing is that it doesn't make these things any more 'true' or more representative of 'reality'. This is why for centuries, atheists have tried to create a science of morality, although the results have not always been liberal.
For example Auguste Comte's Positivism
It was the Church’s power in unifying society, which the Religion of Humanity tried (without success) to emulate. They believed the growth of knowledge was the driving force of ethical and political progress and celebrated science and technology for expanding human power. Rejecting traditional religions they founded a humanist cult of reason. This was the creed of the eighteenth-century philosophes restated for the nineteenth century. If the Positivists were distinctive it was not in their attitude to religion – many Enlightenment savants including Voltaire cherished the absurd project of a ‘rational religion’ – but in their belief that, as human knowledge advanced, human conflict would wither away. Science would reveal the true ends of human action, and – though why this was so was never explained – they would be found to be harmonious. This was the archetypal ‘utopian idea in a modern’ guise, and it was vastly influential... The society of the future would be technocratic and hierarchical. It would be held together by a new religion – the Religion of Humanity.
John Gray, Black Mass: Apocalyptic Religion and the Death of Utopia
Marxist communism would be a more recognisable example of this also.
Many New Atheists avoid discussing the philosophical underpinnings of their worldview. They just assume because they nominally purport to value Reason, that their worldview must be rational. It still relies substantially on concepts borrowed from Christianity though, and these become no more 'rational' by removing God from the equation.
As such many NA, tend to lack self-awareness and critical thinking in their common critique of religion:
1. Religions are 'made up' so they are false - New Atheist ideologies are also made up
2. Believing in false things is harmful - They also believe in false things, and anyway, things are only harmful when they cause harm not simply because they are false.
3. Religions cause unique harms to society - No evidence of that, secular ideologies actually have a 'pound for pound' worse record for violence (even if we leave out generic nationalism).
4. Getting rid of religions will make people more humanistic - 'rational' ideologies may or may not be humanistic, as history has showed. While some Enlightenment thinkers were humanists, humanism was not one of the core tenets of the Enlightenment.
As an atheist myself, I have no problem with people criticising religion when it deserves it (which it often does), but I find NA blanket criticisms to be superficial and based on flawed reasoning. That they do this while holding themselves up as paragons of enlightened reason is somewhat incongruent.