I think some of the confusion comes from two levels of consideration of rationality and Bayesian computations in the brain, which I'll refer to as micro and macro levels, for the purposes of this distinction.
When neuroscientists such as Karl Friston ask if the brain is Bayesian, they are usually referring to the micro scale. The chief question being if there are mechanisms in the brain capable of representing priors and likelihoods in order to compute posterior distributions. At this level, there are promising results particularly around the brains ability to perform near-optimal Bayesian updating to control muscles, for example.
In the more general public discourse, the concern of macro Bayesian rationality is to ask if we're able to make Bayesian judgements in our conscious thinking. The shift toward behavioral economics and away from homo-economicus generally represents an abandonment of this hypothesis. Even the rationality community seems to acknowledge that the best interventions start assuming general irrationality and attempt to nudge it in the right direction.
Importantly, these two are not necessarily in conflict. It's possible for the micro scale to be Bayesian while the macro scale suffers from a wide variety of biases that diverge significantly from rational Bayesian computation.
At an even grander scale, some have posed the question if humans in aggregate (global scale) are capable of Bayesian reasoning. It's possible we're relatively Bayesian at the smallest and largest scales but not Bayesian at scales in between.