Before I found the (non-curebie) parenting subforum here, I was on another one that had a mix of curebie and non.
What did the parents who wanted a cure think it would be? On that board, which was probably representational, they thought would be a diet (GFCF) or medication (yet to be invented) or therapy (such as ABA) that would make their children verbal (if non-verbal) and sociable and flexible.
Interestingly, both curebie and non-curebie parents might do the same thing (such as ABA) but the difference would be in expectations for the outcome. The non-curebie parents would hope the therapy would make their autistic kids move more smoothly through their lives. The curebie parents hoped the therapy would make their kids stop being autistic.
So when curebie parents talk about cure, they are talking about something their kids would ingest (medicine or diet) or therapy(ABA, for example) that would make their kids perceive the world in a more NT way. Clearly no such thing is possible. But it's what they mean by "cure".
If you look at "cure" anecdotes (that involve actual autism and not something mistaken for it) you will see that the child is just as autistic as before but has learned speech, or learned coping mechanisms. Some parents think that autism is rather like an outer layer that can be peeled away by diet, medication or therapy, revealing somebody with typical neurology. This isn't true, but it's a common delusion.