Leaving aside some loopholes that are about to be closed, tests of Bell's theorem rule out local hidden variables theories. But any theorem is only as good as the assumptions that go into it, and one of these assumptions is that the experimenter can freely chose the detector settings. As you know, I don't believe in free will, so I have an issue with this. You can see though why theories in which this assumption does not hold are known as "conspiracy theories". While they are not strictly speaking ruled out, it seems that the universe must be deliberately mean to prevent the experimentalists from doing what they want, and this option is thus often not taken seriously.
But really, this is a very misleading interpretation of superdeterminism. All that superdeterminism means is that a state cannot be prepared independently of the detector settings. That's non-local of course, but it's non-local in a soft way, in the sense that it's a correlation but doesn't necessarily imply a 'spooky' action at a distance because the backwards lightcones of the detector and state (in a reasonable universe) intersect anyway.
That having been said, you might like or not like superdeterministic hidden variables theories, the real question is if there is some way to test if that's how nature works, because one can't use Bell's theorem here. After some failed attempts, I finally came up with a possible test that is almost model-independent, and it was published in my paper "Testing super-deterministic hidden variables theories".
I actually wrote this paper in the hospital when I was pregnant. The nurses kept asking me if I'm writing a book. They were quite disappointed to be drowned in elaborations on the foundations of quantum mechanics rather than hearing a vampire story. In any case, in the expectation that the readers on this blog are somewhat more sympathetic to the question whether the universe is fundamentally deterministic or not, here a brief summary of the idea.
The central difference between standard quantum mechanics and superdeterministic hidden variables theories is that in the former case two identically prepared states can give two different measurement outcomes, while in the latter case that's not possible. Unfortunately, "identically prepared" includes the hidden variables and it's difficult to identically prepare something that you can't measure. That is after all the reason why it looks indeterministic.
However, rather than trying to prepare identical states we can try to make repeated measurements on the same state. For that, take two non-commuting variables (for example the spin or polarization in two different directions) and measure them alternately. In standard quantum mechanics the measurement outcomes will be non-correlated. In a superdeterministric hidden variables theory, they'll be correlated - provided you can make a case that the hidden variables don't change in between the measurements. The figure below shows an example for an experimental setup.
The provision that the hidden variables don't change is the reason why the test is only 'almost' model independent, because I made the assumptions that the hidden variables are due to the environment (the experimental setup) down to the relevant scales of the interactions taking place. This means basically if you make the system small and cool and measure quickly enough you have a chance to see the correlation between subsequent measurements. I made some estimates (see paper) and it seems possible with today's technology to make this test.
Interestingly, after I had finished a draft of the paper, Chris Fuchs sent me a reference to a 1970 article by Eugene Wigner where, in a footnote, Wigner mentions Von Neumann discussing exactly this type of experiment:
“Von Neumann often discussed the measurement of the spin component of a spin-1/2 particle in various directions. Clearly, the possibilities for the two possible outcomes of a single such measurement can be easily accounted for by hidden variables [...] However, Von Neumann felt that this is not the case for many consecutive measurements of the spin component in various different directions. The outcome of the ﬁrst such measurement restricts the range of values which the hidden parameters must have had before that ﬁrst measurement was undertaken. The restriction will be present also after the measurement so that the probability distribution of the hidden variables characterizing the spin will be different for particles for which the measurement gave a positive result from that of the particles for which the measurement gave a negative result. The range of the hidden variables will be further restricted in the particles for which a second measurement of the spin component, in a different direction, also gave a positive result...”Apparently there was a longer discussion with Schrödinger following this proposal, which could be summarized with saying that the experiment cannot test generic superdeterminism, but only certain types as I already said above. If you think about it for a moment, you can never rule out generic superdeterminism anyway, so why even bother.
I'm quite looking forward to this conference, to begin with because Vienna is a beautiful city and I haven't been there for a while, but also because I'm hoping to meet some experimentalists who can tell me if I'm nuts :p
Update: Slides of my talk are here.