I think one of the largest changes would be an overall decrease in economic productivity. Society would shift away from capitalism as many concepts would either be unintuitive to us or aren't possible to uphold with our overall capacity. In practice this would likely mean a reduction or outright elimination of full-time work, which is replaced with alternative options like WFH or the four-day work week. This may impact the open hours of stores but there is a possibility that improved work conditions may mitigate that.

Assuming that this is a society of mostly autistic people from the start rather than a gradual replacement of neurotypical people, it might actually have better outcomes for autistic people as the stigma created by neurotypical people wouldn't exist. Or it would be significantly decreased.

Even many people in medical professions, who would have access to your diagnosis information through your medical records

This is not guaranteed. OP needs to check how their country stores and discloses medical data.

Thanks for the comment. It doesn't seem to have gained much traction yet but it does look promising.