I always remembered Mr Rogers saying kids could tell if he was being fake, that they were smart enough and sensitive enough to notice. Tom Hanks just gives me non-genuine vibes in this role. If I miss Fred Rogers, I just watch his show.
I've reflected on the film a bit since seeing it, and I think some of the "fakeness" is at least partially a dramatic construct. The movie is told from Lloyd Vogel's point of view, and when he's first visiting the set, he's still his hard-bitten, cynical self, looking for a seedy underbelly to peel back and expose. That's why in particular the actress playing Betty Aberlin is so sickeningly sweet when Vogel watches a taping of one of the Make Believe segments — not because she is, but because that's how he wants to see the whole thing. I think when they get away from the show and Fred isn't being Mister Rogers is when Hanks comes across as most genuine; he's allowed to be the person instead of just trying to imitate a beloved TV personality.
Betty Aberlin was in Dogma. I don't picture her as sickeningly sweet in real life. Fred Rogers came across consistently the same in interviews and appearances as he did on his show. I think he was pretty much the real deal. I must admit, the idea of him being a father and what he necessarily must have done to become one is a little difficult to wrap my mind around, but I suppose it's like the idea of your parents having sex.