But how you're describing ST isn't incompatible with religion, only some religions. Nothing about religion itself says that the creators or some higher power need to be an active participant in the human experience.

And how doesn't simulation theory allow for the simulation creator/admin to interfere with the simulation? You don't have scientific equipment recording data on everything, everywhere, for everyone, and people claim to see wild shit all the time. But even ignoring the wild shit, it could be as simple as tripping someone, moving their keys, giving them some disease or disorder, or any of a million things that we can't accurately predict even when explicitly looking for it.

In this instance it doesn't. But in this universe almost every industry using simulations run many different ones with different parameters. It doesn't make sense to assume simulation theory with only a single simulation without interventions, because that assumes the simulator already knew that what the simulation would produce would fit what they wanted and that's not a guarantee (just for information theory reasons alone!)