That’s a long debate, which basically played out between Bohr and Einstein in the 1930’s.
The ontological limitations of quantum mechanics are to do with our ability to define the physical quantites in question. In that regard, I recommend Bohr’s response to the EPR paper: https://journals.aps.org/pr/pdf/10.1103/PhysRev.48.696
The fundamental thing is this, which Einstein was also very clear about: Physics is not, in the deepest philosphical sense, about “reality”. It’s about building models that can account for observations. Einstein was, as I said, completely on board with that and considered time and space to be free inventions of the human mind.
Only he wanted models (theories) to conform to a norm that they posit an external world existing independently of any observer or measuring apparatus. The Copenhagen interpretation is the necessary consequence of the fact that with subatomic physics this is no longer possible, as amply showed by Aspect’s experiments and the ultimate failure of Bohm-like models.
This is compatible with “shut up and calculate”, but the Copenhagen interpretation can in no way be reduced to that.
