And it does. People duck when you throw something at them. People look for cover when it starts raining. They get off the road when a car's coming.
They may profess idealism, but they act like materialists.
Because if you don't, you don't survive for very long.
But don't people also act as if their beliefs could shape the world? I present to you prayers to Jesus and "The Secret" as two of many, many examples.
Further, I don't see a direct link between beliefs and survival, since one of our key survival strategies is acting toward an uncertain future, one we craft and picture by way of beliefs about what may happen. In a very real sense, our imaginations are critical to survival - the hypothesis dies in our stead (as pointed out by Karl Popper).
I'd make the case that it is our mental life - surreal and imagined - that overshadows the mere material, animal lusts, and generates whatever it is we hold to be a good life.