I think when a work of fiction includes an autistic character, they do so to make a character that has different traits to other characters- something that makes them stand apart and be interesting. In order to be interesting, they have to be significantly autistic or have exaggerated or numerous autistic behaviours. Someone like myself, who is on the spectrum to a high functioning degree that my behaviour was caught eventually but I am "normal" enough to merely come off as "strange", would not make an interesting character and no doubt would itself be a misrepresentation of autism because there is such variety to be found on the spectrum- a character like myself would hardly challenge any issue found in more autistic people and would likely be accused of being "too normal" and not worth even labelling as autistic.

I think the main stereotypes are of a completely shut in, antisocial autistic child, usually with savant capacity, or with Aspergers I think most people would immediately think of the Big Bang Theory.