I tried replying to your post, but splitting it into different quote sections was too much effort. :v So, a couple of points:
1. I am well aware that Marxism and the New Atheism are different. I even said that my point was not that atheism per se led to authoritarianism (although in fact I think it does and we are starting to see creeping authoritarianism in the West already.) I simply meant that the Soviet Union demonstrates that human nature, not religion, is the problem with this world. I am not convinced that a world full of new atheists would be a peaceful one. In actual fact, in the 2-3 months that I spent on Richard Dawkins' website, as a religious person I experienced sheer hate from most of them. (It's nice to see that you're apparently not in that category.
I might have tried to have more patience in my last post if I had known you were genuinely interested in a decent discussion.)
In the end, it's a moot point. New atheism hasn't won the day in the West. In Australia, the vast majority of people are essentially agnostics who don't believe in anything very much, not militant atheists. I don't know what the case is in the US, but it's my impression most people are nominally Christian or else agnostic/ atheist without being militant about it. And on top of all this Western birth rates are plummeting (thanks to the sexual revolution and the abolition of the family) while Christianity is booming in the Third World. I don't think Islam will continue into the information era and we're already seeing many Middle Eastern refugees converting to Christianity or atheism. We are currently witnessing the global triumph of Christianity.
It's interesting that you mention Western creeping authoritarianism, because the politicians and parties that are advocates of this (LePen, Orban, Wilders, AfD, PiS) all argue that their measures are necessary in order to protect CHRISTIAN values. They argue that Europe is Christian, and therefore they are defending Christian European vulture from Islam. NO. Contemporary European values may have originated from Christianity at one point, but are actually founded in the Enlightenment. European values rest on secularism. It's very ironic that Islam is indeed antithetical to this, and liberals should be the ones in oppostition and conservatives to give concessions to Islam 
Atheism doesn't have to win the day, as long as organized religion loses out. And it is losing out. We don't care what individual people believe, it's their business. What matters is that religious lobby groups (which are always supported by some sort of organized religious group) lose their ability to enforce their beliefs on others through policy. If people consider standing FOR or AGAINST something based on considerations other than religion, it's a pretty good start.
On a global scale birth rates SHOULD plummet if we want to have a chance at surviving a couple more centuries Earth's resources will simply not be enough to sustain an ever-growing population of humans, even with the advances in agricultural technology. See my previous post on how Christianity in making matters a lot worse by opposing contraception and family planning in Africa.
2. As for your second point, I acknowledge that atrocities have been committed in the name of Christianity. That's not the question. Bertrand Russell said that every piece of moral progress in the entire of history has been opposed by the Church, including the abolition of slavery. That is factually false.
As for the changes I mentioned during the 19th century, Wilberforce was not operating as a lone wolf. He represented a movement of evangelicals who were committed to the abolition of slavery. Look up John Venn and the Clapham Sect. It was Christianity which overthrew slavery. You might also like to look up the commitment of the early Wesleyans to social justice. I have heard it argued that the only reason the UK avoided its own French Revolution was the influence of John Wesley.
Russel could have phrased it differently, but from a global angle he is still right. Wilberforce may have had a group of faithful standing for abolitionism (though each and every case can be argued how much part exactly did their religion take in this), but elsewhere, slave trade itself was driven by Islamic pirates who had no difficulty in justifying their action in THEIR sacred book. In the end, it's the total tally you need to look at and in this regard, religion did FAR more bad than it did good.
3. Yes. "The revolutionaries may have glorified reason, but ended up acting unreasonably." Precisely my point. In fact they deified reason, and it didn't end up helping them too much/
As for advances in medicine, science and so forth, the Enlightenment never led to that stuff. Look up what Albert North Whitehead or Robert Oppenheimer had to say about the influence of the Reformation on producing modern science and society. Democracy flourished in the Reformation nations: the UK, the US, Canada, Australia, NZ whereas there is scarcely an Enlightenment nation on the continent which hasn't been ravaged by totalitarianism over the past 300 years. (France, Spain, Italy, Germany...)
The USA was SPECIFICALLY founded on Enlightment principles, in fact, almost all founding Founding Fathers were Agnostics, Free Thinkers, Deists and very probably in some cases (like Banjamin Franklin) Closet Atheists. They were highly sceptical of organized religion and drafted the Constitution in a way they did PRECISELY to keep Church affairs out of Public affairs, as they knew nothing good can come of it.
You also mentioned Canada, NZ, Australia - where Christianity was mostly represented by the meek Anglican church and its offshoots. To keep it short, the Anglican church was specifically designed to either keep out of state affairs or give its silent support where needed. It thankfully was (and is) barely a political factor and these countries were clearly better off for it.
Modern science was born out of the Christian worldview, because Christianity provides an explanation as to why the universe is an ordered place which behaves according to physical laws in the first place (in that God is a rational and ordered God who made the universe behave according to certain laws, which Christians could then seek out via scientific method.) This is why so many of the early scientists were Christians: Copernicus (yes, Copernicus!), Kepler, Newton, Boyle, Kelvin.
You also have to take the Zeitgeist into consideration. At the time the Church (whichever iteration) was still a powerful entity to be feared, after all not long ago they were still burning heretics at the stake. Of course, no enterprising Natural Philosopher (science is actually an invention of a later age), dared openly question the basic doctrines of Christianity. And true, they might not have even wanted to, after all accepting the existence of God at the time was a given. But to say Christianity was a driving force in the quest for knowledge is a fundamental misunderstanding. It's plain old Human Curiousity that was responsible for that. Religion and Faith were ALWAYS a constraint on that, and you see cultural arcs based of to how relaxed religious doctrines were at the time.