My son loves Sesame Street characters, and "costume" characters... When they're on TV.
However, he's very afraid of them in person. He gets clingy, must be picked up, and holds us in a Death grip.
We've so far just tried introducing him to the characters, usually with a name. "That's Cy, he's a big bird like Elmo's friend."
We also try being pleasant and friendly with the mascots, but it doesn't seem to help.
Other fears, like new kids on playgrounds, he overcomes after 5-10 minutes of exposure. Not so with costumed people.
So far, he's seen Santa Clauses, Easter Bunnies, a Gopher, and Cy the Cyclone's bird. He's been equally fearful of them all.
I'm sure he'll grow out of it, but right now the fear interferes with his enjoyment of the events we're at. We never run into these characters intentionally, but they end up being at family-oriented activities and events. Once he spots them, he seems unable to resume his enthusiasm for the place until the mascot has been out of site for 10 to 15 minutes, which can be a large portion of these events.
My son in just over two years old.