Or, on the flipside, they do end up messing the child's social interactions up. Eventually the child's going to have to come to terms with the fact that being outright furry is not socially acceptable in a lot of societies.
And we have a tendency to associate Furries with tolerance and good ideas, but in all reality, I think there are close-minded and ignorant furries just as there are smart and social furries. Just like all other people.
As for being more social as a furry, I'm a living testament against that. I'm incredibly antisocial. In fact, I believe that a lot of furries aren't incredibly social outside of furry communities (and still open about being furry), because it can be downright fearful to be open about your furness to others who aren't furries.
So all in all, it just comes to the parent's decisions. Just like having two parents that are gay, the child may accept their lifestyle, or may not. He may rebel, he may conform. What the child learns is no different from what other children learn in the home. As for an analogy, you're changing the classroom and the teacher, but it's still the same subject and curriculum.