I don't think there is a consensus among physicists. I think the reason for the lack of consensus is that this issue is ultimately an issue of interpretation of quantum mechanics, and does not have a direct experimental test that can decide the question one way or the other.
Everyone agrees on the experimental facts. In a Bell-type experiment, you can separate two entangled particles so they are at a spacelike separation. Then measurements of the spin of one particle along some axis will be correlated with measurements of the spin of the other particle along some axis (could be the same or different depending on the whims of the experimenter). It also turns out that this correlation cannot be used to send information from one experimenter to the other, and can only be discovered after the fact when the experimenters re-enter each others light cones and compare their experimental results.
The question is, "how do these particles at spacelike distances know to be correlated with each other in the ways prescribed by quantum mechanics?" Bell's inequalities rule out the possibility that a local hidden variable theory can explain these correlations, assuming the measurements are statistically independent. In other words, it is not possible to explain the observed correlations -- correctly predicted by quantum mechanics -- by assuming the particles really do have a definite spin before we measure them (determined by hidden variables we don't know about) and that they only interacted at the point they were created (unless one appeals to superdeterminism).
At this point, different people have different opinions, depending on their interpretation of quantum mechanics. I think probably the "default" view of physicists who don't work directly with interpretations of quantum mechanics would be to take the Copenhagen interpretation, which would imply some nonlocality when one particle is measured, causing the wavefunction of the other particle to instantly collapse. However, other physicists may have other interpretations where nonlocality may or may not be present. For example, according to superdeterminism, the initial conditions of the Universe are such that the experimenters are not free to choose the axes along which they measure spin; the particles really do have spins and the choices the experimenters make are effectively pre-determined in advance to agree with the predictions of quantum mechanics. In this interpretation, there is no non-local process.
For what it is worth, personally I believe there is some non-locality in this process. I suspect that deep down our notions of space and time are emergent from some more fundamental quantum mechanical degrees of freedom, and entanglement is a kind of clue about that. Entanglement is perfectly natural mathematically if you think about Hilbert space; it's only when we add on our notion of how space and time "should" behave that we run into problems of interpretation. However, that's just my personal speculation and if you challenged me I'm not even sure I could define precisely what I mean, and I am sure other physicists have different points of view.