It's possible to make any model deterministic. Used to be just to save the seed, but I'm not sure it still is now that everything is distributed. Maybe a little more effort.
changing the input (data) means you get a different output (model).
source data has nothing to do with model determinism.
as an end-user of AI products, your perspective might be that the models are non-deterministic, but really it’s just different models returning different results … because they are different models.
“end-user non-determinism” is only really solved by repeatedly using the same version of a trained model (like a normal software dependency), potentially needing a bunch of work to upgrade the (model) dependency version later on.