The particular neckbeardy, fedora wearing, Sam Harris listening trend of atheism was a pretty clear reaction to the evangelical psychosis of the Bush administration.
Other geriatrics here can attest that the character of Christianity at the time was way different than it is now. These days, the fascists are more "culturally Christian" and avoid overt bible apologism. But back in the day, these people were constantly on TV spewing young earth creationism and other shit, and they were largely taken seriously. It's hard to believe now how much time was spent "debating" evolution back then. The atheist backlash at least affected discourse aesthetically for some time, making these views laughable, which deplatformed a lot of evangelicals or made them hide their power levels on TV.
Some argue that this brand of atheism justifies imperialism. It does so really only in theory. There really is no material basis for atheists in the US to justify an invasion anywhere in the world. The truth is that Christianity is still a far more powerful force for imperialism. Bush said that God told him to invade Iraq. I don't see any president saying anytime soon that the US needs to secularize a country through force.
If fundamentalist and political religiosity were defeated, then belligerent atheism would dissolve, but the reverse is not true.
Overall, it really does seem like people over emphasize this group of internet no-lifers because of the cultural cringe they manifested.
Except it also did in practice, making this claim categorically false.
New Atheism was a deeply, deeply liberal movement in the way that it worshiped uncritical ideas of "rationality" and "science", which just like classical liberalism can only produce a farce as the ruling ideology increasingly casts itself as "rational" and thereby wins the approval of the self-satisfied chauvinists who were always the base of New Atheism. See Neil DeGrass Tyson's "Rationalia" for an even more recent example of this flimsy approach to values.
It is also the natural and inevitable development of any "movement" so concerned with castigating backwater rural populations and promoting their "universal" values that they would seek to impose these values on other places they saw as backwater. The Islamophobia was therefore not a change in ideology but a change in focus.
The western chauvinism was always there, but my memory of the day to day posting was largely Kent Hovind, "look at this bad take on christian-mom-forum.org", and proto-manosphere dating advice.
At least when I was doing the rounds in the mid-2000s (so post 9/11 and during the main Iraq occupation). I was definitely after the heyday of Usenet channels.
It was always just assumed that Western culture produced superior values to the hyper religious middle East, as can be shown by how we just beat them in a war, but it rarely actually produced that much discussion.