To see if you can overcome your fear, I would use the tip one of the other posters gave, to see them as funny. I would go to Youtube and keep watching the thousands of videos there are of the great things about character meets.
Next would be to understand what it is that freaks you out, if it is in appearance or something else. If it's about getting spooked from behind, keep an eye on your navigator to know where and when they are around. If they are going to be at spot x at 10am, then somewhere at 9:59 a door will open. Of course there can be unexpected moments, but such is life and fearing the unexpected can only be avoided by locking up yourself in your cabin.
And to start slow, start with characters that are very unlikely to jump at you. Characters like Chip& Dale, Goofy, Donald, Stitch, are basically big kids jumping all over the place, loving fun and games. Start with gentler characters like Mickey, Minnie, Daisy, who won't do that.
In my experience, I'm not a big fan of fur characters, I'm not good at non-verbal communicaton. Communicating with something that can only gesture and has only 1 expression makes me feel uncomfortable at certain times. 99% of the time the characters sense this. And the 1% of the time they don't, a character meet is over in a few seconds. And for characters passing you on their way to a meet, they are on a schedule. They need to be somewhere at a certain time.
Last thing to keep in mind: Characters have only good intentions, they are not like your co-workers. They are not out to laugh at you.