Or ever more local differences like when school age cut off is. I would expect some small differences be found due to these impacts, but they would not be universally applicable without generalization.
If schools roll over to the next grade at the start of October, babies born in October will perform better due to being the oldest in their class, but this would not be universal. What I would expect to be universal, is given a school system that does grade division in this way, students right after the division would do better than the ones born right before, as the first group is the oldest in their class and the second group is the youngest.
The extent this pairs with astrology would probably depend purely on population densities between different cultures. If things were fully uniform it would average out, but given they aren't, some residual bias existing wouldn't surprise me.