Ok, yes, very good. If we have at least two rules, then the reverse rules do not have to be causally invariant. I also came up with a single rule example: Consider the rule AB->AA. It is causally invariant for all starting states (can prove). If we start from ABA, we end with AAA in a single step. If we reverse the rule, then AAA can go into ABA or AAB.

I suspect, if we start from a graph (as opposed to a string), we can construct something very similar, although it seems more difficult to prove