As a student of theoretical physics I'm well acquainted with the multitude of crackpot ideas attempting to circumvent Bell's theorem regarding local hidden variable theories in quantum physics.
Recently, however, I've been working on my master's thesis regarding Bayesian probability, and I came across a very interesting paper by Jaynes on precisely the subject of Bell's theorem (E.T. Jaynes, Clearing Up Mysteries - The Original Goal, In: Proceedings, Maximum Entropy and Bayesian Method, 1989).
Jaynes writes about what he calls the Mind Projection Fallacy and its prevalence in quantum mechanics. He claims the fallacy is a result of failing to appreciate probabilities as representations of states of knowledge (epistemological), as opposed to as fundamental properties of nature (ontological); clearly, Jaynes advocates the Bayesian perspective on probability.
Using his 'Bayesian inference as extended logic' approach, Jaynes derives a number of - to me - impressive results in this paper and others. More to the point, on pages 7-16 he explains two objections to Bell's results:
Bell didn't appreciate the difference between the epistemological nature of probability in making predictions and the ontological nature of causality. This lead him to propose the wrong probability distribution for his class of hidden variable theories; one which is indeed (trivially) violated by quantum mechanics.
Bell did not include all local hidden variable theories. For instance, his choice excludes those where the hidden variables are time-dependent.
These objections don't read crackpot in my opinion, and as demonstrated in the linked papers there is a slight historic tendency for the Bayesian perspective to make one see old results in a new light, particularly in other fields of physics.
I've heard that Jaynes is adept at making himself seem obviously right and others obviously wrong - so I may have fallen for that trap - but this argument struck me as something that should've gotten a lot more attention than I'm aware it has. That is, I was still taught the Copenhagen interpretation complete with Bell's theorem ruling out local determinism, which seems to imply that this argument has either not gotten mainstream attention or has been thoroughly debunked.
Are there any obvious counters to Jaynes' viewpoint that I'm not aware of?