Locality in QFT vs "non-local" in QM
The locality of a QFT refers to the operator algebra. The (non-) locality of Bell's theorem refers to the states (rays) of the Hilbert space. These are different notions of locality, and they coexist peacefully.
To quote, Fredenhagen1
Apart from these problems, there is a deeper reason why it is fortunate to separate the construction of observables from the construction of states. This is the apparent conflict between the principle of locality, which in particular governs classical field theory, and the existence of nonclassical correlations (entanglement) in quantum systems, often referred to as non-locality of quantum physics. As a matter of fact it turns out that the algebra of observables is completely compatible with the locality principle whereas the states typically exhibit nonlocal correlations.
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1 An Introduction to Algebraic Quantum Field Theory, from the book Advances in Algebraic Quantum Field Theory.
Yes, QFT is a subset of QM theories – quantum field theories are theories whose observables are naturally constructed from field operators – so everything that holds for all QM theories holds for QFTs, too. In particular, all QFTs are "non-realist" because all QM theories are "non-realist".
QM theories may be in principle non-local but the QM theories relevant for the description of our Universe are local. They're either QFTs or their generalizations like string theory. The locality means that an event or a measurement can never impact or change the probabilities of events that are spacelike-separated. Mathematically in QFTs, this is derived from the vanishing (graded) commutator of fields at spacelike separations.
Everyone who says that there is non-locality in our Universe in any sense is just plain wrong – violates elementary insights of the special theory of relativity of 1905. There is no non-locality in Nature. One may consider hypothetical theories in QM which are non-local but those aren't relevant for our world. In particular, the non-locality in these theories has nothing whatever to do with the right explanation of entanglement experiments.