My MIL was a deputy head teacher fifty or so years ago. According to her, autism 'did not exist' in her days, only 'bad parenting' and 'badly behaved children'.
When my children were young, she would often admonish them for being impolite (e.g. not speaking to her) or for playing with their hands (which they did when they were nervous. She would call them 'rude' and 'spoilt' to their faces, and tell us we were ineffective parents.
We spoke to MIL about this, tried to explain the boys' needs, but, in the end, we decided it was best to keep the boys away from their grandmother because her negative comments were damaging to them.
I feel sorry for my MIL. I am almost certain she is also an individual with autism. She has very rigid ideas and opinions and a massive need to control everything and everyone in her environment. She did not seem to realise the impact her behaviour or her comments had on others. Now she is in the early stages of dementia, this rigidity and control can be particularly intense. Yet, her behaviour has denied her a relationship with her grandsons.
OP, from your posts, it seems that your MIL has a positive relationship with your son, but she may not understand very much about autism. Someone suggested attending an autism awareness workshop with MIL and, I think this may be a really helpful activity, because she could learn strategies that could help to calm your son a little or aid instruction. Once she finds out that autism friendly strategies work, she may begin to accept his diagnosis a little more and stop the parental blaming.