Before we go into this, I want to look at those words "believe" and "accept". They are not the same thing.
More than once when I have got into conversations with Christians, they have announced that all you have to do is read the Bible, and you'll be converted. Just like that. Because to read it is to believe it. Unlike some of them (I'm sorry but it's true) I have read it. All of it. Right through. Not just the sound bites they get in church, but the entire book, and more than once. I've studied it carefully. I do not believe it.
The same applies to some Muslims, they will tell you that if you read the Koran, you'll automatically believe it and follow Islam. Well, I've read that too, and no I didn't.
I've read most of the holy books that exist today, I have some in hard format (that's books to us old folk) and some on CD. I do not follow any of these religions.
I do not believe them. I do however, accept them. I accept they exist, and I accept many things about them, if not all. I certainly do not accept the accuracy of much of the content that purports in its own way to be historical or scientific, while I accept some of the advice contained in there. But I do not believe any of this writing has any divine component whatsoever. For that reason I treat them all equally. The Bible is as good as the Koran, and both are equivalent to the Eddur. How I feel about them varies. Respect? I think some deserve more respect than others. The older they are the more respect they deserve simply on lasting power. All old writings deserve respect, and equally so, be they holy or otherwise. Recent books, such as the Book of Mormon, I have very little respect for. But that's a tangent.
One can accept a book without changing one's beliefs.
When it comes to science the same could be said to apply, and in fact I freely admit that in my biased view if you read "Why Evolution is True" by Jerry A. Coyne, you will believe it, but for totally different reasons. Coyne's book does not require anything other than logic to be believed, and let's face it, if you don't believe in logic you have real problems.
But it doesn't matter if you don't believe it, because in this case accepting it is enough.
A problem arises when a person thinks he cannot "accept" science, because science doesn't care whether you accept it not. If you don't believe in germ theory, as some minority religious groups don't, that won't stop you getting infected. The germs haven't heard that you don't believe they are infectious, they simply didn't get that memo.
Not all religious people refute science, in fact it's probably only a small percentage overall, but they are a dangerous minority because more moderate, open-minded members of their own religions are not comfortable criticizing them. So, when a fundamentalist in Texas demands that creationism be allowed to be taught in school, other Christians who are perfectly happy with evolution, let them get away with it. They don't see the harm in it. Be nice to our more conservative brethren, they insist.
Is it harmless to teach mythology alongside (or indeed in place of) science? We'll leave that one for another day. The question remains as to why it is demanded.
There are those who say that they are equivalent beliefs. Is science a belief? It certainly isn't a belief system. It is not a religion, not by any definition (and there are several.) It is not written in stone, in either sense. Science is a collection of knowledge, it's "what we know so far." This is why it changes.
Some religions, such as the Baha'i Faith also allow for change over time in teachings, and moderate versions of other religions will concede that what we once understood as "truth" has been replaced by something broader.
It is this change that the fundamentalists oppose. They do not accept (note use of word there) that when their holy books were written, some things were not understood the way they are now. This is why you get apologists who spend half their lives explaining the inconsistencies, contradictions, and inaccuracies in said books. Instead of shrugging it off and admitting that 4000 years ago maybe people really did think bats were a type of bird, they create convoluted explanations about what the word "kind" really means. They'll delve into the etymology of the Hebrew. I can play that game too, which is why using the exact same methodology I can prove that God's name is Asher. Ask me about that some time.
But here's where we get to the image above. There is absolutely nothing in the Theory of Evolution (thank you Sherry Loveland for pointing out that it's Theory with a big T) that prevents you believing in God, and many experts in the field are theists. Evolution doesn't cover creation at all. It doesn't mention it. That's a whole other area of study. Evolution and creation are not actually opposing theories. It's just that the hardcore creationists insist that everything that exists now was created in 7 days. More moderate creationists claim that there has been evolution since Noah's Ark, which still doesn't make them evolutionists, because it doesn't happen that fast. They've misunderstood it.
What these folk have in common is Young Earth Theory. This is a theory that the Earth is only about 6,000 years old, give or take (there are quite a lot of different ages proposed) and there simply wasn't time for evolution as taught by science to have occurred. So either it didn't happen, or it happened really quickly.
But there are plenty of people who accept the scientific evidence both that the Earth and everything else in the Universe is billions of years old, that life on Earth began 3.5 billion years ago, and has been evolving ever since, and it doesn't affect their religious beliefs at all.
The issue is not a theist vs, atheist one. It never has been. This is in effect a damning accusation by Christian fundamentalists. In their view, if you don't agree with their version, you are an athiest. Presumably they'd level this accusation at the Pope. When pressed they will admit that in their view he's not a real Christian. I know because I've pressed a few.
No, they don't think you are a real Christian if you accept the Theory of Evolution. And this is what people are afraid of. They are afraid that if they accept the logic and evidence of science they are not real Christians. They are afraid that their families, friends, and congregation might disown them (that is a pretty scary idea). But most of all they are scared that God will know. Being omniscient and all. And obviously, in their version, this will make God angry. Therefore accepting science is risky. So, you know, best not read it, just in case.