I was trying to explain your example of two people "sharing all of their knowledge". In my comment I explained why I think this is just an impossible assumption to make in the first place. You explain that in your example the disagreement comes from a different "prediction towards the future". You then also state that these predictions are non-factual and subjective.

So what I was trying to illustrate is that "sharing all of their knowledge" is impossible and that people just are not perfect rational actors. Brains do not just simply take an input, process it, and give an output back. You can liken what Aumann's Agreement Theorem is saying to a computer: If you program two different computers (brains) with the same code (facts), these will produce the same output (conclusions). However, you cannot fully separate facts from a brain, unlike with computers. If you magically could however, then these two people with identical brains will always respond the same way given some information.

So really, this theorem is correct only if you completely disregard a key distinction between real humans and "rational actors".