The repository pattern doesn't necessary lead to dumb objects.
If the objects have no logic outside Save/Update, you're probably doing too much outside the object.
Idealy, you should never use properties to get data from your object, compute things, and put data back in the object. This is a break of encapsulation.
So the objects should not be anemic except if you use simple DTO objects with CRUD operations.
Then separating the persistence concerns from your object concerns is a good way to have Single Responsibility.
