The rule "BA" -> "AB" is presented in Section 5.9 of the Physics Project book ("The Significance of Causal Invariance") as being causal invariant. The instances of its causal graph shown therein for 5 time steps and initial condition "BBBAA" is given as example, showing that all 5 instances are isomorphic to each other.

I've run the example with the MultiwaySystem function (ResourceFunction["MultiwaySystem"][{"BA" -> "AB"}, "BBBAA", 5, "CausalGraphInstances"]) and the function output matched the book content.

However:

1) Running the system for only 4 time steps, not all instances are isomorphic to each other, since in this case there 2 types of graphs (among the 5 instances) which are clearly not isomorphic to each other.

2) In the subsequent example in the section -- that changes the initial condition to "BBBBAAAA" -- the MultiwaySystem function couldn't generate the instance causal graph shown in the book, regardless of the number of time steps I tried (from 4 to 10). Actually, for all these time steps different graph types are generated which precludes the existence of isomorphism among them all.