Asserting that a particular causal model is an accurate description of the universe certainly constrains experience to fit the causal model. Asserting that it is possible to accurately describe the universe with a causal model is tautologically true because a fully connected model fits every possible probability distribution. Asserting that it is possible to accurately describe the universe with a simple causal structure constrains experience to match a simple causal model. If you know that the universe fundamentally works by running some causal model, asserting that the universe runs this particular causal model predicts that you will never find a more accurate causal model for describing the universe. I'm not sure how asserting that the universe fundamentally works by running some causal model would constrain experience.