Though the first few iterations of evolution were rather shaky, such as Lamarckism, and even Darwinism, Punctuated Equilibrium has an extremely large range of data supporting it. Not to mention that studies in the Galapagos (probably spelled that wrong) as late as the 1990's showed short term genetic variance and a change in one species of finch as a whole in just one season of drought.
The components of the nerve system have many of the same components, though configured different, in almost every organism that isn't technically a plant. I won't bore you with all the details, but I'll leave at it's widely supported.
Now, evolution is not a religion, despite the fact that some people use it like one. For one, the theory of evolution is constantly changing, just like every aspect of science. Secondly, the theory is woven into every area of science as we know it right now, whether that be psychology or astronomy.
Contrary to belief, it is possible to believe in evolution and believe in a religion. Darwin himself was a devout catholic and at the time of his research was studying to be a clergyman. The reason that the theory of evolution, and science in general, excludes or dismisses religious theory is because it has to. The existance of a god or a great here after, right now, at least, is not quantifiable. If it is not quantifiable, it cannot be tested. If it cannot be tested, it cannot be included. Science and religion are not mutually exclusive, but must be studied seperately out of necessity.
In any case, that is my round about way of saying it should be taught, as it is the base for many other sciences, and is in no way affected by seperation of church and state as it isn't a religion.