You have to ask yourself what do you mean by science and what do you mean by religion. The definition for religion (from the dictionary app) is a particular philosophy of life or conception of the world, and the definition for science is observing the world around you and coming to conclusions based off of observations, experiments, and evidence. Now, I can’t see how these two are opposites, can you? Why would one have to live with one and without the other? It seems to me that you cannot have one, without the other. How can someone observe the world around them and not come to hold any worldview (science with religion).
If you are using the common meaning of the word religion, theism (the belief that there is a god), then what makes theism and science opposites? You would be suggesting that people who do not have atheism (anti-theism) as their worldview are narrow-minded and, therefore; their worldview is illegitimate and not considered “science”. The real question should be a world without theism, or a world without atheism (not “science” as you call it), or the question could be a world with science, or without it (obvious answer).
On another note, to the atheists reading who think that their belief is the only “science”, you certainly have small grounds to stand upon. Based off of observation, experiments, and evidence, evolution and other atheist beliefs hold no ground. Specifically for evolution, there is no way to observe macroevolution (an animal evolving from one kind to another kind), as it would take too long. Your experiments that you use have failed through the centuries (experimenting with life from non-life, finding fossil evidence, etc.), so now atheists have created their own “experiments” which are rigged to give them what they want. For an example, what makes carbon dating so useful? Why have scientists suddenly used carbon dating? The method is highly unreliable and often dates things such as volcanic rock and recently dead plant material to be millions, or billions of years old.
Now to evidence. You would think that of all of the intermediate species, there would be at least a couple remaining fossils of a fish-human, or a frog-cat, but there isn’t. Not even one! You can invent more evidence (conveniently weak, dissolving fossils theories for all of the intermediate links) for all of the inconsistencies, or you can throw away your bias and look at the real question: a world without atheism or without theism; a world without science or without non-science.