I can tie my shoes.
My AS son could tie his shoes in kindergarten (his school reinforced the skill with him daily and often throughout the day).
But then, in first grade, we got him slip-on shoes and he forgot. Part of the way through first grade, we got him tie shoes again. But his teacher wouldn't let him wear them because he couldn't tie them independently.
So, now we are in a rut. We work on it at home but probably not as much as we should. (He's now going into 3rd grade).
Because of that experience, I've told my daughter (risking kindergartener) that she will wear tie shoes everyday in kindergarten and 1st grade. After that, she make other choices. But, I want the skill ingrained first. (She may not have trouble, she's NT and has already taught herself to tie little bows in her dresses.)
I think it may be more difficult for those the spectrum, but if you can carry out a sequence of actions in other scenarios and have the fine motor ability required to pinch strings and move them, I don't see why it can't be learned. Might take a significant amount of repetitions. Might not be ultimately worth it. But, I don't see how it's universally impossible.
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So you know who just said that:
I am female, I am married
I have two children (one AS and one NT)
I have been diagnosed with Aspergers and MERLD
I have significant chronic medical conditions as well