I've noticed people can be offended when you refer to them by their adjectives. E.g. "blacks" instead of "black people", "autists" vs "autistic people".
One term encourages the idea that they're people first-and-foremost, with the adjective used to describe a particular subset of people.
The other removes the emphasis on them being people and is pretty depersonalizing.
As you can imagine, it's much worse when it's a historically marginalized group--as an example, fewer people will care if you say "blondes" vs. "blonde-haired people".
My understanding is that people object to this as it is a means of defining them rather than describing them. In fact, I know people who would be insulted with the use of "autistic people" as opposed to "people with autism"
The other removes the emphasis on them being people and is pretty depersonalizing.
As you can imagine, it's much worse when it's a historically marginalized group--as an example, fewer people will care if you say "blondes" vs. "blonde-haired people".