This brings up a question that is of course contentious, but what is the limit for disability accommodations and are there cases or limits where a theme park just isn't appropriate for some people?
Someone said that a theme park is, by definition, a place where you will be waiting in line for much of the time. When should someone say, this isn't a place for me?
It's not for the theme park operator nor random people on the internet to decide what is appropriate for a child with developmental disabilities. It's the parents, and in cases where their input is possible to procure, the child. Everyone should have the chance to have a good time, and that's what the ADA ensures.
The ADA also ensures that the same mentality can't be used as a cop out by, for example, grocery store owners, to make their stores inaccessible to wheelchairs. Without the ADA, the excuse "the store isn't a suitable environment for customers in wheelchairs because the aisles are too narrow, nothing we can do, sorry" would be perfectly fine. Thanks to the ADA, they have to make the store wheelchair accessible. Many stores have also sought to be inclusive of customers with developmental disabilities by having "sensory friendly" hours in the mornings or evenings where the lights are adjusted and the music turned down/off.
At the end of the day, is Disney an "appropriate" place for an autistic child? Maybe, maybe not. That's not our decision to make, nor is it Disney's. Disney's role is to make their experience accessible to these guests, not make judgements about what they can or cannot handle or what would be appropriate for them.
There have been lawsuits asking for accommodation above and beyond. Arguments that autistic kids should be able to do what they want whenever they want with no wait times ever. Walking by Peter Pan and the kid wants to do it right now? Walk on in. Kid wants to ride Pooh for an hour without getting off? That must be allowed. If that is what is necessary for that kid to experience Disney on their terms, is that reasonable?
The ADA does not contemplate "above and beyond" accommodations, and lawsuits seeking them have routinely failed. Heck, even cases where the plaintiff was asking for quite reasonable accommodations have failed. Nobody is expecting for the guest to be able to access an attraction instantly, like you describe, nor would it be reasonable for any guest to expect that of Disney.
If I had a special needs child who could not handle a wait elsewhere for Peter Pan like you described, even if it meant seeing a show, eating lunch, or whatever it may be, I personally would not bring them. But that's my judgement to make as the parent.