Speak your truth quietly and clearly.
Like us they seek to abolish every belief (or non belief) that is not theirs.
Firstly, not every atheist wants to abolish every belief/non-belief that is not theirs. Secondly, there is only one belief that it is conceivable that all atheists might want to abolish... the belief in gods. The only thing any two atheists necessarily have in common is that they both lack belief in god. There are actually many other things that are way more important than atheism to many atheist's world views such as skepticism and freethought to name a couple.
As for your questions:
1) The same thing/s that makes atheism different from any other religion out there today.
2) The same things we are collectively doing right now... informing, confronting, criticizing, educating, and so on.
3) I don't see how in your scenario the new/militant/radical whatever you want to call it atheist definition would change.
Pillage and burn.
Pillage and burn.
1) It depends on the specific issue at hand- but it likely stems from not "believing" the basic premises of the new religion - probably claims about a god/supernatural beings, forces, etc
2) It should be countered, criticized and exposed by rational argument wherever its influence arises- unless, of course, we are talking about the Church of the Flying Spaghetti Monster
3) See 2
May you be touched by his Noodley Appendages. Ramen!
May we all be touched by his noodley appendages! The world needs pasta! A great pasta awakening/revival!
But this is constantly going on already. There are always new sects rising, it is a lucrative business don't you know. They can internationalize thanks to internet pretty quick, making video's, publishing and distribution of books, cd's and dvd's is very easy and cheap. Indoctrination of large numbers of people has never been more easy in all of Earth's history and yet - I think - it is very improbable we will see the birth of another full blown religion. There are several reborn Jesuses wandering the Earth at this moment/ at every moment, all with their own devotees, all with their own grandiose declarations and all stillborn sects. Some already retreated in seclusion, Jim Jones like, headed for infighting, psychological and physical abuse or worse. Much worse. Others remain more engaging with the world for the time being. UFO's and extraterrestrials are a big hit in the sect business too.
But they do have the serious disadvantage that none of them are true. None of them see doubting the articles of faith as a virtue, everyone of them is in conflict with science one way or another, even those who more or less (sort of) abstain from supernaturalism.
Their public speakers for as much as they have them - different engagement strategies are applied - rely on charisma much more then intelligence. They have to because they do not appeal to intellect or ratio since that's a losing proposition by definition: they're not selling something intelligent or rational, instead they appeal to emotion, existential issues: fear of life, fear of death, meaning etc.
There is no equivalence, basically atheism is the default. It is what is left when all the bullshit flies.
As Becca points out, atheists don't want to abolish different beliefs. At least, they typically don't want to do so in the same manner as religion has used. You are engaging in false equivalency by framing it that all beliefs are equally deserving. What is the difference between a flat-Earther and a science teacher that is abolishing beliefs about a flat Earth by showing the evidence and science around our knowledge that the Earth is an oblate spheroid? Knowledge and the ability to come by knowledge is perhaps the most important legacy we can pass on to new generations. Treating it as being equal to religious fantasy is an intellectual crime that should not go unanswered for.
Another quiblle is this notion of "New Atheism". The only thing "new" about it is that the internet has provided the ability to form communities that have emboldened atheists to come out publicly and has helped greatly to proliferate atheist views into the mainstream public. No longer do atheists need to hide their lack of belief and no longer do we need to sit back quietly while being bullied by a theistic majority.
What makes us different? Well, that depends. Many atheists are atheists by way of Skepticism. In that case, the difference is that Skeptics apply critical inquiry to their beliefs as much as they can. They hold in high regard the scientific method. And how do we know the scientific method is the best tool to evaluate truth claims? Because it works and nothing else comes even close. But, not all atheists are Skeptics and not all atheists have come to their conclusion for good reasons.
What should atheists do about it? Do about what? Atheists should continue to speak up and speak out. As should anyone who cares about anything, including theists. Let the strongest ideas reign supreme on the battlefield and exempt none from taking part.
Should we follow a New Atheism definition? As I've stated, "New Atheism" is a misnomer and I don't agree with your definition of this generation of atheists or that all atheists can so easily be lumped together (nor should they). Otherwise, yes, atheists using science to inform beliefs and refusing to remain silent about those beliefs are two things atheists should continue to do.
I am not a new atheist, and do not identify with the New Atheism. I pride myself on not trying to take away anybody's beliefs, but I do think it's vital to inform people about how they, with their beliefs, dismiss mine and try to take mine away. If there is anything militant about my atheism, it is the passion with which I oppose any religion legislating its beliefs into society as a whole. I do feel rather like a cornered wolverine about that, and I will not stand idly by while it happens.
If this "new" religion is based on the supernatural, then it's bullshit.
If this "new" religion is based on pseudoscientific woo, then it's bullshit.
As Rationalists and Atheists, we need to put on our bug ugly rubber swamp boots and stamp out Bullshit.
A "new" Atheist is just someone who doesn't stay quiet. WE SPEAK UP!
"Though wise men at their end know dark is right,
Because their words had forked no lightning they
Do not go gentle into that good night."
Neither will the 'new' Atheist go gentle into that good night. Hitch was a good example of this.
2- We should repeatedly point out that this is exactly what EVERY major religion tries to do, and that it's exactly what the religion you just left did. This new religion was just more successful at it, and you fell for it. We should go on to point out what this new major religion does to those who do not believe in it (after all, one religion cannot dominate without racking up a kill count) then ask them how they think that's what god would want to happen.
And from that I would explain that nobody knows what god wants. Notice how I'm not taking a strong atheist standpoint; they would not listen. I would go on to state that if a god were real nobody could know what it demands from us. People do not need religion to live a good life, and that's all that is important. If the god they believe in is as just as they think then you shouldn't need to be part of an organized religion to please said god. If you just life a good life that should be good enough.