Evolution is a scientific subject, but sometimes it seems to be the subject of more non-scientific debate than genuine scientific discussion. The most fundamental debate over evolution is arguably whether evolutionary theory contradicts or is incompatible with religious beliefs. In an ideal world this question wouldn't be relevant — no one debates whether plate tectonics contradicts religion — but in America, this has become an important question. However, the question is also too broad.
Diversity of Religion & Religious Beliefs
There is no such thing as "religious beliefs," without context or content. The term "religious beliefs" or just "religion" describes a very broad class of beliefs and belief systems, a class which contains within it an incredible diversity of ideas and positions. What this means is that it's impossible to sensibly, fairly, or truthfully say whether evolution does or does not contradict religion or religious beliefs without specifying what religion, what form of what religion, and what religious beliefs one has in mind.
So, the only way to really answer the question is to say: sometimes yes, sometimes no. Evolution does contradict certain religious beliefs and even at times, certain religions. Evolution is also readily compatible with other religious beliefs and other religions. Evolution can contradict some forms of some religions but not other forms of the same religions. Indeed, it should be noted that there does not appear to be any contradiction between evolution and any one entire religious tradition.
The reason for this is that any large religious tradition with much of a history behind it will contain enough variety that even if there are groups which object to evolution, there will be groups which either welcome or simply ignore evolution. Sometimes this multiplicity of ways in which a religion can be interpreted may be a source of embarrassment — after all, it is hard to claim a religion to be True when there is so little agreement as to just what the religion really is.
On the other hand, it is also a principle of evolution that those individuals which are best able to adapt to changing environments are the most likely to survive, reproduce, and pass on their genes. Perhaps it also true for belief systems — those with the widest internal variety are best able to adapt to changing social circumstances and pass themselves along to succeeding generations. It may be difficult for some religions and some religious traditions to survive in the scientific environment of evolutionary theory, but not impossible.
Natural Selection vs. Supernatural Agency
Despite all that, though, there is one possible basis for arguing that there may be a fundamental contradiction between evolution and religion — but only insofar as science generally may be incompatible with religion generally, or at least supernatural religion. To be more specific, the contradiction lies in the methodologies of science and supernatural religion: science relies upon a naturalistic approach while supernatural religions eschew it.
Not all religions rely upon supernatural causes, beings, or realms, but they are common and insofar as they exist, they are described as having some sort of impact upon our universe — whether it's the creation of our universe or some ongoing relationship. Such an impact would, in principle, be amenable to scientific investigation but religious adherents insist that their claims must be believed on faith. Some make attempts to find ways to apply scientific investigation to supernatural agency — like Intelligent Design — but such attempts are universal failures.
It's not the case that science is somehow incompatible with every system that fails to apply scientific methodology, but not every system purports to make empirical claims about the nature of our universe. It's the nature of the claims which is key: any time a person makes empirical claims, they are making claims which can be subjected to scientific scrutiny. If you don't apply scientific standards of evidence and belief to those claims, then you are deliberately rejecting the most fundamental principles of science. If you also reject science, then you're consistent, but if you try to accept science when it comes to other empirical claims, then you are participating in a contradiction.