To the best of my knowledge, there is no hard and fast rule about this. Some kids can wash and rinse their hair at six and some women like to have someone else wash their hair for them at sixty! Personal grooming can actually be a social behavior that is a form of bonding. It might even be an enjoyable, soothing and connecting experience for a mother and her daughters.
However, you do say that your sister "will not allow" her girls to wash and rinse their hair. It could be that she wants to be sure they are squeaky clean and not left with suds in their hair. But,there is little to go on in terms of your sister's reason.
So, I would say this. If not allowing the girls to do their own hair is indicative of a more general over-controlling situation, or a more pervasive situation in which the kids are not being able to become age-appropriately independent, then there might be more cause for concern.
The other reason for concern would be a boundary issue regarding the actual circumstances in which the hair is being washed. If a mother is in the shower with teenage kids, for example, then this is not so much a question of hair, but more question of appropriateness.
However, if there is not a boundary issue or over-control issue here, then it is purely your sister's business as to when her kids wash and rinse their own hair.