Shrodinger qualified his statement, perhaps not strongly enough, in saying it is far more radical in quantum mechanics.
Put another way, reality is very slippery with little bitty things, but make things much bigger and reality conforms to our perception of it.
So, with the exception of certain equipment we use, we can treat solid objects as if they are solid (even though they are almost entirely empty). They will behave, except at relativistic velocities, the same way Newton said they would.
And when you get down to the quantum level, they still follow very solidly defined physical laws, it's just that the laws are statistical. That's why quantum entanglement at a distance is not a way to transmit information (that plus the fundamental reasoning behind special relativity).
So it is dangerous to mix philosophy and quantum physics, because quantum physics doesn't generalize into the realm where we can perceive things (for the vast majority of phenomena).
But if you want to get philosophical, the implications of quantum physics on the idea of cause and effect is certainly interesting.