I think the lack of understanding regarding autism can be the cause of this. Employers may not know they are discriminating against someone with autism in some cases. Now if you disclose your autism and you are fired, have your hours/days cut it can be pretty clear. Sometimes we may reveal our autism when applying and get rejected. Or at an interview and we didn't get the job. Sometimes the co-workers not understanding can be the cause.
I think employers may get the impression that the person needs a ton of adjustments and maybe less liking to hire them. Even though the ADA (Americans W/ Disabilities Act) states employers much provide reasonable accommodations.
Clarify what is expected of the job- Provide more details as to what the person will be expected to do on the job. Also, make sure on the job description you are clear as to what is expected from the employee.
Make sure your instructions are concise and specific- Make sure you are more clear with your instructions. provide more details. Don't assume the person can read between the lines. Instead of saying 'it's your turn to bring doughnuts,' specify what place you want the person to buy the dessert how many doughnuts to get, etc. We are forgetful because our brains are like your son/daughters messy room, be sure to send them a call/text to remind them and make sure they respond to you.
Provide sensitive but direct feedback- Most autistic people don't pick up on social cues (facial expressions, body language, motions etc) Example: I can make a nonverbal gesture saying 'no' and the autistic person will look at you like they have no clue what you're doing. If they completed a task incorrectly, don't go off on them. Make sure your feedback is positive but constructive.
Be reassuring, not condescending in stressful situations- we tend to get overwhelmed and stress in certain instances. Provide some info on what to do if something goes wrong. Example: if the printer breaks here is the extension to call Joe, the repair guy. It would help if the person had a buddy to take over if the person gets overloaded and needs to cool off.
Just because someone is different doesn't mean they are any less. Maybe if you stop making up fanstises in your head and actually put in the effort to make reasonable adjustments you will be amazed and what someone can do.