Does every rule have causal invariance?

No. Causal invariance is a special property a rule either has or lacks — most rules don't have it. Without it, branches could split and never reconcile, so different observers or orderings could end up in incompatible worlds with no fact of the matter about what happened. [setup] The project's interest is in rules that do have it, plus the open question of whether near-invariance might still yield approximately consistent physics.