The position advocated by person 2 (on your posted website) is 'non-overlapping magisteria', short NOMA:
http://en.wikipedia.org/wiki/Non-overlapping_magisteria
The problem with it is that it's wrong. If sciene can't say anything about it, why on earth would theology be capable of contributing anything new? Admittably, there are scientists who hold this view (including Stephen J. Gould who coined the term), yet they obviously lack the epistemological understanding of why the scientific method is so important. In my view, such people may be good scientists 'in the lab', but not in the true, philosophical sense (I see good philosophy and science as closely linked together).
Take for instance the infamous case of Francis Collins (head of the human genome project), who turned to Christianity after seeing a frozen waterfall that reminded him of the trinity. What is going on there? It's an interesting case of double-standards, if one of his scientists came to a conclusion about science in such a way in the lab, Collins would most likely personally fire him!
Yet there are also other positions apart from NOMA. There are scientists who believe science validates God. Now this view is definitely smarter than the above, but it's also most likely wrong. All the 'design' arguments have been discredited so far, and there just isn't any other tangible evidence for any sort of God.
There's the interesting phenomenon about lots of physicists being deists. But you also have to be careful there, first of all, most of the time their beliefs have nothing whatsoever in common with a personal God. In some cases it hardly even qualifies as deism. When Einstein said 'god doesn't play dice', he just meant the elegant order of the universe. I find it an interesting semantic phenomenon that physicists keep referring to such principles as 'god', when in fact they have nothing in common with Yahwe or any other religiously based god figure. Same with Hawking, who now finally distanced himself from the god mataphore.
Not to forget, according ot a 1998 survey, 92% of the National Academy of Sciences physicists are still atheists, so the 'many religious physicists' only make up 8% in that field. Still, it is more than biologists (only 5.5% believers), for the obvious reason that evolution shows how complexity arises spontaneously, thereby destroying and even inverting any form of the ontological argument.
http://www.stephenjaygould.org/ctrl/news/file002.html
Kenneth Miller, a very smart biologist that, among other things, testified in the Dover trial in favor of evolution, wrote a book called 'Finding Darwin's God'. In it he tries to first convince creationists that evolution is right. I'm pretty sure that because he himself is a Christian, and because he uses excellent arguments (including theological ones for why a creationist god would be a fraud), his book is much more convincing to creationists than Dawkins' 'The Greatest Show on Earth'. So that part of the book is good. But now comes the problem: in the latter part of the book, Miller starts to babble about esoteric interpretations of quantum mechanics. He's not a physicist! This illustrates the desperate attempts of rationalization for religious scientists. This isn't scientific! Miller would be appalled if some physicist claimed to have found God in the 'intelligent design of nature'. Not to mention that even many theologians would have serious problems with Miller's descriptions of his god.
Altogether, it can be said that while religious scientists do exist, they're being fundamentally untrue to the scientific method.
By the way, I used 'atheists / agnostics / non-believers' interchangably because to me they're effectually identical; the only difference being how the people interpret their own disbelief. Are there people agnostic about the tooth fairy? If yes, they're in the same sense agnostic than most agnostics AND atheists are agnostic about god.
It's often said that you can't prove god nor disprove him. I agree that you most likely can't prove god, that's cus he most likely doesn't exist. If he existed, one could find evidence for it.
And obviously in most cases one can't prove a negative. Yet I wouldn't even go as far an a priori accept that god is non-disprovable. Clearly, a squared circle is disprovable because of internal inconsistencies. Apply that concept to the definition of 'god', and depending on the definitions there are lots of huge inconsistencies! More to this approach here:
http://www.americanchronicle.com/articles/view/110595
Sorry I didn't mean to write the essay for you haha. I'll look at the comments at the website you posted again, maybe something else worth mentioning will occur to me.