Ah, job searching. I can certainly empathize with you there, so let me start off by saying I'm sorry for what you're going through. I had a similar struggle myself for the first two or three years or so after graduating high school. I won't go too much in detail, but long story short - I applied for a number of retail stores that never got back to me. Countless applications. Two different callbacks. Two different interviews for two very different companies (not on the same day or week). Got hired for one.
'This will be fine. There are lots of cashiers/sales floor employees/retail employees in the world. How hard can it be?' I thought to myself.
I had about a week or two to train. Training was very fast, and I was expected to do quality work under a very short period of time, with very little room for error. I watched fellow co-workers hired around the same time frame master the job, even enjoy their job, and making it look effortless, while I was walking into work nearly as confused as I was on the first day of training. I did my best, but it was not enough; they let me go. (It really depends on the employer and the company - not all are like this, or so I hope; this is just my personal experience with retail. Not putting down retail by any means. Retail is a great job for the right person. I just wasn't the right person.)
I learned valuable lessons from that experience:
1) Retail is not for everyone. It is competitive. You are expected to fit in with your co-workers, you need to be able to solve simple and complex problems quickly, and you need to be able to easily connect with customers and coworkers alike. Good communication skills are not just an ideal - they are a must. Make sure you know exactly what you are applying for; really take the time to read the job description and make sure it's a good match for you, because otherwise it's taking a risk that you may get hired, but will be miserable in your new job position.
2) If being on the autism spectrum is going to be an issue to your work performance, you need to let them know. Had my retail employer known why I was struggling, the employer may not have hired me in the first place, because they would have known I was the wrong fit for the job, and not the neurotypical I may have initially appeared to be. Either that, or they may have been more patient and understanding of my condition, and known to work around it.
[Employers generally look at employees objectively (whoever is going to boost their company). If you have a bowl of soup, you're going to want a spoon, not a butter knife. And if you've got a piece of toast and some butter, you want a butter knife, not a spoon. If you apply for a metaphorical bowl of soup but you're a metaphorical butter knife, then of course you are going to be swapped with a metaphorical spoon. It's not to say that you're not good enough. It says your skill set is better suited to either another company, another employer, or another type of work. Find your butter and your toast, as it were]
3) When considering the job application of a potential candidate, yes - employers are thinking about your job experience. But what they also really want to know is this: Is this a person I would want to work with every day?
4) At a job interview, you could ask the interviewer if the company is willing to work with people with mental disabilities, or people on the autism spectrum. You don't have to specify that the person is you. I mean, you can - it's up to you. But it is a perfectly reasonable and valid question.
Sometimes I feel like I have the social skills of a rock. I didn't do so well in retail, wasn't happy working it either. But the next job I interviewed for (dishwasher) - I told them about my Asperger's. Fortunately the interviewing hiring manager saw my potential and was willing to give me a chance (despite my limited experience at the time). And I'm pleased to say that the job is something that plays to my strengths, and I rarely have to speak to anyone; am currently still employed. Usually work independently. Most days fairly predictable.
So, I guess what I'm trying to say is that it's possible that retail isn't the right fit for you, and if not, that's okay. Chances are, there is a field of work that actually needs someone with your potential and skill set. But yeah - went through a ton of rejection, so you're difinitely not alone in that respect.
Have you looked into: Kennel Technician, Host/Hostess, Dishwashing, Bussing, Prep Cook, Baker, Pet Groomer, Florist's Assistant, Warehouse, Stocker, Dental Lab Technician, Dog Trainer, or the likes? Some of these jobs don't necessarily require schooling, are constantly in high demand, and allow for growth if you feel so inclined.
Best of wishes on your job search.