...being very handsome, and very like himself, her influence had always been great, and they had gone on together most happily.
For these two reasons alone, I think.
They get on well together, being similar.
Anne is different, and here I see fatherly and sisterly feelings not playing a great part - the *type* playing a major role.
So it's not that they don't like her, or think she's done something wrong.