You're thinking along the right lines, I reckon. Many people seem to imagine this single thing called "intelligence", and never really stop to think how many different kinds there can be. Or, they assume that if you have one kind of intelligence, you must have all of them in equal measure. I don't do too bad for the "academic" kind of intelligence, but my social and emotional intelligence is way behind - when I do something dumb socially, people seem to act like someone as "clever" as me couldn't ever make that kind of mistake - "how on earth could you not know that!" I sure don't feel "clever" then, whatever my school exam results might suggest.
The stereotypes about autism are a big problem too, I think. Autism is so often shown as one extreme or the other - either children with severe learning impairments or "eccentric" geniuses, depending on the purpose of the message (raising charity money, getting employers interested, making a nail-biting TV drama, or whatever.) I think that is slowly improving, but things which are extreme are often easier for people to remember because they stand out more.
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When you are fighting an invisible monster, first throw a bucket of paint over it.