Within simulations, probably most of the impact comes from simulations that are created to decide which civilizations should get more resources outside the simulation, and not from sims run for random entertainment purposes.
If we are in a simulation, simulators might be extremely different and incomprehensible to us. “Entertainment” and “to decide which civilizations should get more resources” are just two reasons, there’s probably many others that it’s hard for us to even conceive of?
This being said, these kinds of unknown unknowns probably don’t change the upshot from our point of view.

I think Caro would say that LBJ didn’t just change his mind. Eg he frequently claims that “power reveals” (see also here). And IIRC he describes LBJ as already caring about racial inequality when teaching poor Mexican children in Cotulla.
I’m not sure how much to defer to Caro on this.