The universe as a whole is NOT deterministic as Quantum Mechanics proves. QM is based on true randomness (obvious a simplification but go with it for this conversation).
The fact that the theories that describe QM are based on true randomness does NOT mean that the universe as a whole is not deterministic.
First, we already know that QM is limited, because it doesn't account for gravity. Second, even if QM as it is formulated today did accurately describe the universe to the best of our ability to measure it doesn't mean that another theory that is deterministic couldn't also describe the universe.
Many of the arguments made on the basis of QM go beyond the actual math and are just fairly subjective interpretations of the implications of the theory. It might be established that you can't measure the position and velocity of a particle with arbitrary precision, but that doesn't mean that a particle doesn't have a precise position or velocity. QM tends to be formulated in terms of describing what you'd get if you performed an experiment. That doesn't necessarily mean that the universe actually works in this way.
Think about it - how could you even prove that a given chain of events was or wasn't deterministic? You can't ever reproduce the same chain of events perfectly, so it is impossible to test. That means any claim that there is or isn't determinism in nature is basically unfalsifiable.