Short answer: it depends on your religion.
I suppose it would be wise to describe what science is.
Definition (from my computer’s dictionary): the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment.
This isn’t very illuminating – it leaves unsaid what the scientific method is, namely: to create hypotheses of the structure and behavior of the physical and natural world and test them through observation and experiment.
After a bit of thought, one should realize the following details: the only scientific facts are the results of observations and experiments, an explanation of some event in the universe that fails to permit a testable prediction is scientifically useless, and true scientists are folks that are always trying to disprove current theories about the world.
How does this relate to religion? The most important relation with religion involves the requirement that an explanation makes testable predictions. If your religion of choice includes the conviction that “the world is controlled, at least in part, by some supreme entity”, then nothing can be predicted, because everything depends on the whim of said supreme entity.
Thus, if your religion has such a conviction, then your religion asserts that science is ultimately pointless. Now technically, that doesn’t clash with science, but who wants to be told that their outlook on life is pointless? And the flip side? The scientific method, in requiring that an explanation make testable predictions, essentially declares that a religion with the above conviction is useless. Also, not technically clashing.
So, if you presume that people don’t like wasting their time with useless or pointless endeavors, you arrive at the long answer: science clashes with those religions which assert the ongoing action of a supreme entity.