We can't look at quantum mechanics and call it irrational. The way the universe works is by definition the right / correct / only way. If logic points one way and reality points another, the logic isn't taking everything into account.
>Rationality is something that makes sense for us
But I say:
Rationality is something that makes sense.
So nature cannot be irrational. For instance: we had the very logical Newtonian mechanics. But Mercury's orbit did not make sense. Later on Einstein saw another layer of logic that put both Newton and Mercury in more context, and now both make sense again.
When we see things now that make no sense, it indicates faults in our mental models, not in the things.
In the context of a person behaving or thinking "irrationally": their brain is just atoms and chemicals. It has to work right. If their behaviour and thoughts do not line up to reality, that's a feature of said brain.
Perhaps the irrationality is due to the brain giving too much weight to certain factors, or perhaps they are in fact behaving perfectly logically given what they know and you don't. Perhaps its workings can be improved in software, or in the next hardware generation.
But there's no spooky mechanism that can't in principle be modelled and implemented in a different architecture, ie, transistors.
Why? You assume nature must be comprehensible to us because you define it that way? Nature's not under any obligation to us.
> If something seems irrational, that's because there are rational things layered on top of one another in a way that creates a misapprehension in a partially-informed observer.
Possible irrational things: Collapse of the wave function, consciousness, why anything exists. There's also non-computable functions, paradoxes like the liar paradox, and the inability to refute various skeptical possibilities like living in a simulation.
Combine that with the fact that all models are wrong, some are just more useful. We can't model the entire universe with perfect accuracy without the model being the universe, which means there are always things left out. Our rational explanations are approximations.