But you can get differential aging without any difference in acceleration, so it does seem right to say that acceleration is not the cause of the differential aging. An analogy: Suppose you have two substances in the same lab that are burning at different rates, and you want to figure out the cause of the difference in burn rates. It would be wrong to say that the difference is due to the presence of oxygen in the lab, even though it is true that there would be no differential burning (or any burning at all) without oxygen.

ETA: Perhaps this just devolves into a semantic debate about what we mean when we say "the cause". In the Pearlian framework it seems more natural to talk of multiple causally relevant factors without singling one out as "the" cause. And I admit that the presence or absence of acceleration is a causally relevant factor in the twin paradox. I guess my point was that "acceleration" is not the best explanation for the differential aging. There exists a more fundamental explanation that accounts for many more cases (i.e. when neither observer is inertial, or when the space-time is multiply connected), and allows a precise calculation of the extent of the effect. I think its a useful heuristic to single out the most explanatory causal factor as "the cause" if you want to play that game, but like I said, that's a semantic point.