I think there are a couple of points to this. Autism started out as a medical or psychological diagnosis. Whereas the folks behind the LGBT term explicitly created it as an umbrella term in the beginning, with the intention to include as many folks as possible.
Within LGBT, it's possible to apply multiple labels to oneself - as in your examples (an asexual transexual or an aromatic lesbian).
This used to be possible inside of the autistic spectrum to agree as well, but the labels were less clear. E.g. What was the difference between Aspergers and autism? Where do folks who have non-verbal learning disorder fit on the scale - or is this the wrong scale? Do we count folks who have BAP (Broader Autistic Phenotype)? While high functioning autism vs low functioning autism was easier to define, it was taken as insulting.
So eventually everything just got the one label, but that blurred the differences. Which made it somewhat more difficult to talk about.