Even in non-relativistic quantum mechanics, entanglement is no symptom of any non-locality. The explanation of the entanglement as a non-local effect is a mystification spread by numerous popular books that ultimately boils down to a misinterpretations of quantum mechanics by Albert Einstein who misleadingly called entanglement "the spooky action at a distance".
Even in non-relativistic quantum mechanics, entanglement is just a correlation – expressed in the most general way that quantum mechanics allows (so it allows different, more general predictions than correlations predicted from a classical theory) – and this correlation isn't the same as causation. Recall: correlation isn't causation. So in reality, there are no signals whatsoever being sent in between the two entangled particles while they are being measured. Instead, the correlation between their measured properties is caused by the common origin of these two particles – by their mutual contact sometime in the past.
When we talk about two entangled faraway electrons or two entangled faraway photons in non-relativistic quantum mechanics, the Hamiltonian is usually assumed to be the sum of the two free Hamiltonians for the two free particles – there are no interaction terms operating in between the two particles at all! Because there are no interactions, there is no influence, and the observed correlations clearly can't have anything to do with any non-local interactions. They all boil down to the initial state that was prepared to be entangled.
Quantum field theory makes it totally manifest and universally valid that there can't be any non-localities. After all, experts sometimes use the term "local quantum field theory" for what may also be called just "quantum field theory". The perfect locality of QFTs is shown by the vanishing of certain propagators in the spacelike-separated region or, more precisely, by the vanishing (anti)commutators of fields at spacelike-separated points.
What Bell's theorem shows is that local realist theories predict correlations that are, in some cases, smaller than the larger correlations predicted by quantum mechanics (and seen experimentally). So local realist theories are excluded. Most of the popular writers about quantum mechanics are deeply confused about this point and they assume that realism "can't possibly fail" so it must be the locality that does fail. But this is a completely wrong, safely excluded possibility.
In 1905, we learned relativity that has guaranteed that locality is a perfectly valid law of physics, a principle that any newer theory obeys (faster-than-light influences are equivalent to clearly forbidden influences changing the past; the equivalence is achieved by the allowed change of the inertial system). The description of entanglement isn't incompatible with locality and quantum field theory actually prohibits non-locality of any kind. Instead, it's "realism" – the classical intuition that the state of the physical system has some "objective properties" even before the observation – that is wrong. The fact that the quantum description of the reality doesn't contain any "objective properties" of physical systems prior to the measurement isn't arts, isn't open to some "personal preferences" or "interpretations". It is one of the basic, fundamental, indisputable, universal postulates that underlie all of quantum physics which pretty much means all of modern physics.
Any "classical model" that would attempt to simulate the predictions of quantum mechanics would have to be non-local to achieve the sometimes high correlations. But Nature isn't described by any classical theory so this is not a problem. There's no need for classical models to be right and they are not right. Nature is described by a quantum mechanical theory that is, by definition, fundamentally non-realist. Quantum field theory is a quantum and therefore non-realist theory that is also perfectly local because it is Lorentz-covariant.