Unless there is some sort of randomness involved, perhaps from the probabilistic nature of quantum mechanics.
Noise from quantum mechanics are a bunch of orders of magnitude too small to affect the brain. Just think what thermal noise would have done to it, have this not been the case.
A regular CPU have a clearly defined set of inputs, a well understood internal state storage, and so on. You can easily set it up to be in some exact state. Any noise introduced would result in it either not working properly or not being large enough.
A brain, on the other hand, have trillions of inputs, and it's state is spread evenly across it.
It's properties can change from the tiniest chemical changes in the liquids going through, from how much the neurons fired recently, and so on.
Some actions would change it's configuration - the neurons forming new links and breaking the old ones.
The magnitude of the problem of getting it to some exact starting state is enormous.
Thus comes the appearance of it's unrepeatability.
But if you were to overcome all that difficulty, then it should repeat itself precisely.
In addition, capturing the 'state' of all of the particles in the brain is not possible according to the UP.
Why would you need the state of all the particles?
You don't need the state of all the particles in a transistor to know it's state, and neurons are quite a bit larger.
Why do you think that observing from outside the universe would not be an interaction?
Because if it was an interaction then the observer would, by definition, be part of the universe.
Think of this as asking an emulator about the content of a memory cell vs having the simulated CPU execute a read instruction to get the data from the same cell.
The first does not disturb the simulation in any way, the second can not be done without detectable disturbing.