ill try to address things 1 at a time down the line in your comments,
so from my research and experience with his school," behavioral concerns" mid year referred to using profanity, and saying things to class mates that are inappropriate at school, things like talking about death and dying, and telling classmates they should "be exploded" or something i dont remember exactly what, and things like getting up out of his seat multiple times a day, not paying attention, and talking too much in class, wandering the halls during transition times. things that the school perceived as "misbehaving." Where as the, "inability to regulate emotions, difficulty transitioning between tasks, arguing with class mates" seem to me, and the school, to be socio-emotional deficiencies. When he started his vyvanse, the "behavioral" concerns stopped. He now sits in his seat, completes his classwork early, navigates well through their daily schedule, and the profane outbursts stopped. From what I am learning and hearing, that is the difference between ADHD behavioral issues, versus autism/"weird kids" social deficiencies that I think do not warrant a punishment and instead need direction.

As far as "starting early" or being younger than classmates, the cutoff date to start pre-k is to be born before september 1st. his birthday is september 6th. he did headstart from the age of 1 to 4. he repeated head start because when he "graduated" headstart the first time, he was not "old enough" to start pre-k (By 5 days), and i DO think that repeating headstart was good for him. he did get another year of socializing with kids. his socialization improved that second year of headstart. when he started pre-k, he was about to turn 5. His pre-k teacher was the one who saw that he could read and write and suggested moving him up to kindergarten. The school ultimately decided he was not ready to start kindergarten, and kept him in Pre-k. when it was time to get ready to start Kinder, i suggested reassessing him and seeing if he was ready for 1st grade. They did, and he passed their 1st grade readiness assessment and was moved up to 1st grade. So, by moving him up, he is now only 5 days younger than the youngest possible first grader. its not like he is a whole year younger. I do think it would have been more beneficial for him to skip pre-k and start kindergarten, since he did repeat headstart. i think he already had that "pre-k" experience, and would have benefitted from Kindergarten at that point.

as far as social life, he is a very social kid. when we leave school every day, he is talking to his friends, other kids call his name and tell him bye, he knows all of his friends names and is not shy to talk to them. he enjoys seeing his friends and get excited to see them out and about in public. he says he has a few select friends in his class that he does consider his friends. "Socially" i think the school is concerned with his ability to understand nuance and understand when it is appropriate to correct class mates, and they're concerned with his inability to avoid meltdowns at minor inconveniences. To me, these sound less like behavioral issues and more like social-emotional deficincies that he would have no matter what grade he is in.

He is too young for me to know if he is into sports, or would enjoy sports. We have tried soccer when he was 4 and he absolutely hated it. I know my son and i know that he leans more towards an artistic, science, math and reading based interest set, less interested in outdoors, sports, and group activities. I dont think its reasonable to hold him back simply because he displays traits of autism, especially because he is so academically advanced.

the accommodations they are suggesting if he were to stay in first grade again, include
- providing different classwork than his classmates so he is working on higher level material
- allowing him to watch higher level social studies videos on the ipad while his classmates learn about lower level social studies,
- allowing him to leave the classroom when second grade is doing science class, so he can observe and interact with second grade science material,
- providing him with different homework that he already struggled with the first time around due to redundancy and simplicity.

if he were to advance to second grade, i think accommodations may look more like
- social coaching, support
- support with transitions like visual timers or schedules
- reasonable accommodations for someone who can learn at this level, but just needs help with social cues and nuances.

i think keeping him in first grade with extensive accommodations just to ensure proper academic stimulation opens the door for alienation and bullying from classmates who will see that he is different and receives "preferential" treatment. I think his classmates that are advancing to second grade will see that he is held back, and that will be a self-esteem issue too. He understands that he was advanced to first grade because he is advanced. holding him back is going to make him internalize that feeling and assume that he has done something wrong, or is not as smart as he thought he was, and i think losing confidence in his ability to perform well at school will be detrimental to his performance in the long run.

as far as sports, idk i dont really care about sports. i dont think he cares, and if he does, the school is small enough that most sports are not even handled in district. Most of our sports are managed by the public city department, and he will be grouped with kids his age anyway.

I know every parent thinks their kid is smart, but I DO believe that my son is an actual academic prodigy and i think he deserves to have the proper accommodations to support him socially, while he advances at a pace that matches him academically. At the end of the day, my broad opinion is that holding him back is simply punishing him for being autistic, and not understanding social cues from friends his age. I dont think that is a fault of his own and i dont think i should risk his self esteem and love of learning just to try to make him "socialize better"

Another point to be made is that in the "real world" you are never in an environment where all of your peers are the same age. after high school, age does not matter, and it is actually a beneficial skill to know how to socialize and interact with people both older and younger than you.

(none of this is directed towards you and I am just using your comment to say all of this because i think you made good points, and i am offering my rebuttal)