It's nothing weird. In fact, it's pretty common.
It's probably also the same reason, say, some people would be frightened of animatronic puppets, clowns, or anything that has a masked face and moves in an erratic or unusual way. Seeing something cartoony or otherwise bright with unnatural coloring behaving in a human-esque way sends off all kinds of "nope" alarms in many people. For some it might be because it's an inhuman creature behaving like a human (I was fully unable to watch the Wizard of Oz as a child /solely/ because I was deathly terrified of the Cowardly Lion and the flying monkeys). For others it could be the simple fear of the unknown - you know there's a person underneath there, but you don't know who, and the lack of true identity itself can unsettle some. (Also, people under mascot costumes are incapable of speaking or at least rarely do by my experience...having a lack of voice to identify it from doesn't help either.)
I'm thinking this seems a lot like a PTSD Stress Cup metaphor. Personally, when I see a mascot, I kind of cringe, but I slowly adjust to it. For someone with PTSD, perhaps the anxiety or stress of the unknown upon seeing a mascot could trigger a fight or flight response in some.
PostEdit: Come to think of it, regarding the voice or the lackthereof, maybe that's the reason why I've met a few friends who told me they were scared of mascots, but okay with, say, Seasame Street. The puppets in their worldly setting seemed to fit, and they had voices to identify them with. That's just speculation on my part completely though, just a random thought...