Since birds are prey animals, they tend to get scared of the most random things! My cockatiel is no exception. I have a fluffy scarf that I wear on the coldest days (it's very warm), but I can't put it on where Buzzy can see it, or else he freaks out. He also doesn't like it if I wear a hat near him, and I have a few colorful shirts that I can't wear around him. New toys also make him nervous - he'll hiss at them for awhile until he figures out that they're harmless. He's still scared of a bell I bought him over a year ago - I can't put it in his cage.
For those who have or have had birds, what are some random things that scare (or scared) him or her?
Most pet birds can easily become scared. Loud noises of any kind is the most common source of fear for pet birds at home.
I do not believe your birds freaked out by a hat the way you think.
Many years ago I have watched something on Animal Planet about a scientist got close to a wild eagle. The eagle got used to her presence and would see her as friendly. As soon as she started to wear a hat, the eagle didn't recognize her any more and tried to attack her when she got close to the nest. I believe your birds weren't scared of the hat itself, but rather they see you as a stranger when you wear a hat. Animals without good sense of smell might use the appearance to define individual human beings. What we wear might become a part of our appearance to some of them.
Yeah, that could be it! For awhile, my bird would look at me suspiciously if he saw me without my glasses. We have a silly little greeting we always do, and he would very tentatively do his part of the greeting if I went into his room bare faced. I'd respond, and he seemed to eventually figure out that it was still me with or without the glasses. However, now I'm wondering if many he just thinks "no glasses" me is another person that he just eventually learned to trust.
My lovebird is terrified of the little noise that my computer makes when I adjust the volume. I have Windows 8, and when you make the sound louder or quieter, it makes a little "ding!" He hates that ding! He will shriek at it. Now I plug in headphones before I adjust the volume.
He also hates the notification noise that Facebook makes when you receive a new message. I have to make sure the computer is muted if I get a message, or he screams and hides in the corner of his cage.
I think he had a bad experience with these things, somehow. Maybe his breeder played these noises when giving shots or something? I'll never know. He just really really hates them.