We took our son right before he turned 2 and were prepared for him to be petrified of the characters. Before the trip, he was always super anxious and nervous in public settings (going to the store with him was tough) and if a stranger (or even most family members) approached him, he'd scream in fear.
When we got to Disney though, he LOVED the fur characters. Spent 10+ mins hugging, pointing, and holding a conversation with Pluto through gestures and babbling. He actually started talking on that trip, whereas beforehand, he had only ever said about 5 words, very sparingly. He even loved the characters he had never been exposed to before in shows/tv/books like the Pooh characters.
On the other hand, like several other posters, he was still uncomfortable around most face characters. The only exceptions were Rapunzel and Flynn because they both went out of their way to slowly approach him and interact with him. They started at a distance making faces at him, then came closer after a few mins and Rapunzel started tickling him and Flynn showed him where he had hidden the crown in his bag which intrigued him. With the other face characters, he would still get nervous if they approached.
I think for some, face characters are scary because they are too real. They look like regular people and if the kid is scared of strangers, then it's frightening being approached by one. With fur characters, that same kid may not be as afraid because they look like a big stuffed animal. All kids are different though.
