In the west, science and reason go together like peanut butter and jelly. They're often spoken as just one word, and more often simply taken with one as a token of the other: to be scientific is to be reasonable, to be reasonable is to be scientific.
But they're different; at times very different. And so at times it's necessary to point out that difference, which is what I'm doing right now.
Both science and reason are truth systems, by which I mean they are ways of obtaining truth* about the confusing world we exist in. We humans spend a lot of time worried about the truth, and as such we have a lot of truth systems, in which I would include: religious faith, common sense, cultural prejudice, trusted teaching, direct apprehension, instinct, intuition, and so on.
So we have lots of truth systems? What are they? How do they work?
The basis of reason is logical progression. We take a pre-existing set of things that we know to be (or are willing to assume to be) true and we proceed from there to use logic and rational argument to extract new truths from them: "Socrates is a man, all men are mortal, therefore Socrates is mortal," and such. At its most formal, there's little room for disagreement provided we start with the same set of truths, in practice, there's a lot of conflict and argumentation in the tradition of reason.
The basis of science is direct apprehension of reality. Particularly, the direct apprehension that can be repeated by multiple observers. If something is sensed enough times, it can be admitted as a true value. These truths can then be used (via intuition or reason or any process you want, really) to produce theories about reality, which can in turn by tested by direct apprehension. The key to truth is not a mathematical construct: it is the perception of reality that forms the core of the truth.
That these two things are not the same is pretty obvious. For one: science is a lot more expensive than reason, and a lot more of a hassle in terms of establishing truth, and even a little muzzy about what constitutes "truth" at all (science does not have eternal truths.) And, indeed, reason and science conflict on many points. They conflict most recently on the issues of quantum mechanics, relativity, and identity**. These are not unresolvable conflicts, but to resolve them, we have to hold one truth value above the other.
For those that value reason above science, quantum mechanics and even more so general relativity are "just theories" that will clearly be superseded by something compatible with the rules of logic, which are after all the form of ultimate truth. Despite the fact that these theories are proven to be correct to absurd orders of magnitude, the think that an ultimate explanation will be revealed to countermand them***.
For those that value science above reason, well there are those that just shrug and say, "well, it doesn't make sense but that's how it is." But for those who value reason (professional reasoners, for instance) who nonetheless take science as a prime truth system, there's a whole world of new types of logic that go by the name "Dialetheism:" the prospect that there can be statements which are both true and false (or neither true or false, or sorta true and sorta false.) Dialetheism is a ... contentious topic in philosophical circles, to say the least.
So, basically, it's fine to use two different truth systems (in fact, in practice, I think that we use all of them at once, all the time) but if you want to have a definite idea about reality, you need to decide what trumps what. Someone who holds reason as paramount before science reaches a very different conclusion from the double-slit experiment as someone who holds science paramount above reason. This isn't necessarily about their profession: there are plenty of scientists who hold reason (in some form) above science, and are excellent scientists. There are also plenty of philosophers who hold science above reason, and are excellent philosophers†.
Indeed, there are lots of other cases of using multiple truth systems at the same time. For instance, a good theologian will use reason and spiritual faith and religious doctrine at the same time.
I think any discussion of modern (by which I mean post-enlightenment) atheist movements has to be able to make this distinction between science and reason, because one can be atheist with a grounding in reason, or atheist with a grounding in science, and these two things mean very different things.
I may be deploying my own prejudices here (see note below about bad theologians; I'm running into that problem) but my hunch is that the scientific atheist doesn't necessarily care one way or the other about the non/existence of God††.
From a scientific perspective, the non/existence of God is a completely boring question: unless God is something which can be directly apprehended within the bounds of controlled, repeatable experimentation (He ain't) then there's no scientific question. Scientifically speaking, God neither exists nor doesn't exist: science has nothing to say on the matter.
From a logical perspective, God must be shown to exist or not exist. For someone who argues that God has been shown to not exist, the idea that others would still believe that God exists is somewhat offensive. People are believing in God irrationally, and if they just understood that they were being irrational, they would stop. I think from here springs the impulse of evangelical atheism: it's damned frustrating to have people persist in irrational belief, right in front of your eyes. You really want to shake them and make them realize the truth. It's also very tempting to conflate this belief with irrationality as a whole, and thus (if you're a sort of person who believes that an ultimately rational society is also an ultimate society) with a whole variety of social ills.
Next I want to talk about the social history of liberalism and fundamentalism. Boy, that's seriously above my pay grade. Ah well, I'll give it a shot.
* Let's make a note here: truth, in this instance, is not necessarily something abstractly true, but something to believe. When talking about truth systems, it's hard to talk about something being abstractly true. You will rapidly arrive at the question "true to whom?"
** I say "most recently" because this is not the first nor the last time that they've clashed.
*** I'm representing, as best I can, actual views of actual people who I have had arguments with. If you don't agree, then you don't agree, but I'm not trying to paint you into a corner. There are definitely those that hold this opinion (or who I misunderstood completely), I'm talking about them, not you.
† Indeed, this is a strength shared by both science and reason: they are instrumental. You don't have to believe in them to use them, even to use them very well. Compare to an theologian. If you don't believe in a religion, it's very hard to be a good theologian of that religion.
†† I realize I'm implying that science / logic show that God must not exist. I'm not, though. I'm trying to take the perspective of two different types of atheist, so that's a baseline assumption.
