That's not how I experienced it, but I can understand why people felt that way. There was a pugnacious straight talking aspect to it that bifurcated into both woke snark politics (via freethoughtblogs) and reactionary debate bros & evopsych gurus, and Guardian TERFs via skepticsinthepub I believe.
I was coming out of Christianity at the time, and you could see a pattern in Dawkins’ targets, on the Christian side he’d only go for poor whites or Africans with the energy of religion is bad because these people are dumb. It’s the same way Gervais always made Karl Pilkington the butt of his jokes.
He famously went for Ted Haggard and George Bush so I don't think I agree with that.
I'm sure there were a bunch of interactions with the Archbishop of Canterbury too.
Ngl I think that period of 'new atheism' was really needed to boost the need for open critique of religion in the much more homophobic and Christian supremacist Bush era and with EMB Islamism taking off worldwide again.
The internet made it harder for reactionaries of that time to control ideas and societies, and people could finally escape these horrible cults in a trend that has not reversed. These are positive developments although reactionaries have since thoroughly ruined the internet now too.
The early 2000s era had Bush pushing apocalyptic evangelicalism, the Catholic church spreading aids across Africa by lying about condoms, the child abuse scandal, and 9/11 all going on at the same time - it felt like the lunatics had used polite society to stifle debate and force respect/submission.
Naturally this also caused anti-muslim bigotry, libertarianism and anti-migrant attitudes in some (e.g. Pat Condell). Nü Atheism never promised political alignment outside of secular principles. It wasn't great at spotting its own cultural biases, and spawned grifters and clout chasers.
This is where I think people get things wrong. Movements don’t spawn these types of people, these types of people spawn movements. Your Pat Condell’s were always anti-Muslim, Nü Atheism (and other movements) just gave them the platform and language to promote it. Same way sex pests become feminists
I don't think ideology is that straightforward - there will be some of that but generally it's multifactorial and directionality is all over the place because it's an individual product of experiences and culture.