Asperger Syndrome was named for an Austrian pediatrition who sheltered autistic children during the reign of Nazi Germany by arguing that they were intellectually gifted. At some point, he and some Catholic nun even built a special school for them. Unfortunately, there was another guy by the name of Kanner who also did research on what was called "autistic psychosis," and Kanner treated the disorder more as a disease. Because much of Hans Asperger's original work was lost during Allied bombing of Germany, though, Kanner's ideas held sway in Western psychology for several decades before it came to light that some autistic children seem to perform excellently under slightly adjusted educational routes.
Because Kanner's thinking persists in some circles, many autists are either left entirely untreated or treated similarly to autists who are obviously mentally ret*d, and this can have a catastrophic impact on the attitudes of parents and teachers toward autistic children, even lead to intentional or unintentional abuse. One of the most logical outcomes is a very simple one: because many autists rely extremely heavily upon the skills they learn in the pursuit of their narrow interests, suppressing the development of these interests in some misguided effort to "cure" them could result in autistic adults who still can't function normally, and they don't even have the skill or drive to fend for themselves in the modern workforce.
Because most autists today would perform at or above the level of their peers in a parallel curriculum that would cost the taxpayer either nothing or next to nothing, especially compared to trying to give their personalities an all-out makeover, many high-functioning autists are very disgruntled over the continued disease-centric perception of autism. Autists are not just disease-ridden pity cases: most of us would perform at or above the level of our peers with only minor adjustments.
To put it simply, I think the concern of Autism Speaks' detractors is that the organization is giving the public a very one-sided, stigmatized view of autism and autistic-spectrum disorders. The propagation of this stigma is making life very difficult, even insufferable, for many relatively high-functioning autists. The long-term effect of orgs like Autism Speaks is to remove a tumor by killing the patient.