Of course we can't prove anything about possible future non-human brains, but try to think about it this way.

Is there a limit to the number of consequences that a single action can have? If you think about all possible future consequences, then the answer is clearly no. Using an example from another comment, opening a closed door could bring you to your death, which has infinite consequences for your (potentially future) family.

Therefore, if rationally analysing each possible consequence takes any non-zero amount of time, deciding any action rationally would take an infinite time. You could try to rationally decide what is the maximum amount of time you can spend on each choice, but deciding that amount rationally would require infinite time.

This isn't a proof, but this consideration comes from spending a lot of time thinking about rationality and AI.

I think you're conflating two thing: solvability and rationality. Your example shows that nothing may be completely solvable, because the cost of calculation is too high. It says nothing about the universe being fundamentally irrational.

The problem I had in mind is if it's possible, for a human, to decide what to do in each situation based only on rationality.

I wouldn't know how to define if the universe itself is rational, in an absolute/abstract sense.

They were referring to present time, not a hypothetical future of more complete explanations of nature and more powerful human brains for conceiving and storing them.

That said, there is a reason why it may not be possible: human consciousness can only exist at a higher level than the most fundamental level of nature, and on that basis, consciousness may never be able to perceive enough of the fundamentals of nature to be able to formulate a complete explanation of it.

However it's not really relevant to the topic at hand. I'm sure humans will always use cognitive shortcuts like ideologies in order to navigate our daily experience, for reasons of speed and efficiency.