Now that I've gone on record as saying that science and religion do not contradict, I should support my point. One step at a time. First step: evolutionary arguments against religion are some of the poorest arguments out there.
Argument 1: Evolution explains too much
I will start out by conceding that evolution certainly contradicts some religious beliefs. If a religion claims that evolution is not true, then obviously it is contradictory to evolution. But how widespread are these beliefs? And if they are widespread, are they really essential to the religions?
The basic conflict here is that evolution fills a gap that was previously filled with God. It's a fairly important gap, the origin of species. But there are so many ways around this.
Getting around this argument results in what is usually referred to as "theistic evolution". I know most of you mainstream new atheists out there probably think theistic evolution is silly, but you probably also think the rest of religion is also silly, and it's really a matter of whether theistic evolution is any sillier than the rest of religion. If it's no sillier than the rest of religion, then evolution is not a useful path to criticizing religion.
Theistic evolution says that God was the one who put this "natural selection" process in motion. God is like the master puppeteer of evolution, rather than a manual laborer who slowly "designs" organisms one by one. Thus, God was the creator, and yet he has no scientific consequences. You can have your cake and eat it too! All you atheists ought to be agreeing that God has no scientific consequences. After all, the reason that science rejects the "scientific theory" that God created the universe is that it makes no predictions, and is thus not scientific. Now, there is a whole line of arguments against such a non-scientific God, but we're only considering the argument from evolution. Did the argument from evolution, by itself, get us anywhere?
Of course, there are those who would reject theistic evolution for a more denialist position. Well, I guess their religion is truly reliant on ignorance. But it's not as if the only alternative is atheistic evolution. As irrational as you might think theistic evolution is, you can't deny that the view exists, and is apparently satisfying to many people.
Argument 2: Evolution is imperfect
Of course, theistic evolution kind of misses the point. The real argument from evolution is that natural selection is awfully inefficient, and involves death and suffering. If God were truly good, he would have organisms intelligently designed, rather than using this makeshift process of natural selection. Basically, the argument from evolution is a subset of the problem of evil.
Now, the reason that atheists think that evolution is a damn good argument against religion is because they don't think there's an answer to the problem of evil. In their imaginations, they bring up the problem of evil, and then the theists all start sputtering. That's certainly what it sounds like. To the atheist, none of the answers to the problem of evil are particularly satisfying, and most seem to be products of cognitive dissonance.
But it is incorrect to say there are no answers at all. Most, if not all, religions have a built in answer--Christianity blames original sin and free will; Buddhism blames ignorance, greed, and wrath; Jainism blames the bad karma that sticks to your soul when you step on ants. No, I don't think these answers are plausible (though it helps that the last two don't believe in omnibenevolent gods). But the point is that people have been thinking about this since these religions were founded. People continue to vary these answers, think up new ones, or otherwise rationalize the lack of an answer. They have enough to satisfy themselves, if not enough to satisfy the atheists, and that's sufficient to render the argument from evolution impotent.
And what does evolution add to the problem of evil anyways? Yet another example of evil. It's not even a particularly special example of evil.
The only thing special about it is that, to a scientist, it's in your face. That's why we have people like Dawkins who claim that evolution was the clinching argument against their religion. Many people don't think too much about the problem of evil, until they encounter the theory of evolution. As a result, evolution appears to conflict with religion. Really, it doesn't present much more of a conflict than does seismology.
If you've answered the problem of evil to your own satisfaction, evolution has no conflict with your religion. If you haven't answered it, then why should evolution, specifically, matter? Even if you don't believe in evolution, it's quite obvious that the world is full of death and suffering, little of which has an apparent human cause or underlying purpose.
The other major conflict between evolution and religion is that Darwinism supposedly leads to immorality. Of course, it's only the ID/Creationists who believe this, and my intended audience is on the other side of the fence. So I feel no need to argue the point.
This is a very complex debate, so perhaps I forgot some other important conflicts. Can anyone think of any others?
Edit: I decided to add one more argument in Part 2.