Since there are disabilities, such as autism, which may make compliance with the CoC difficult, what steps will SE take to make sure they are in compliance with the ADA, and what reasonable accommodations can we expect to see?
I am not a lawyer, but the CoC is likely compliant with the Americans with Disabilities Act (ADA).
The relevant section that Stack Exchange (SE) needs to be sensitive to is Title III – Public Accommodations. The major complication here is going to be ensuring that,
Entities subject to Title III must make reasonable modifications in policies, practices, and procedures that deny equal access to individuals with disabilities, unless the modification would fundamentally alter the nature of the goods and services provided. This includes providing auxiliary aids when necessary to ensure effective communication. Goods and services must be provided in an inclusive setting, unless separate or different measures are necessary to ensure equal opportunity.
Given that the CoC allows for gender-neutral language to be used, and moderators and community managers should start by generally warning users of violations, it would be difficult to demonstrate that SE is not making reasonable modifications to their practices.
I'm not a lawyer, but I usually guess the outcome of lawsuits correctly. There is a circuit split on the issue of whether the ADA covers websites, so certainly in the circuits that hold that the ADA does not cover websites1 SE is in compliance.
For people with disabilities in circuits that have held that the ADA applies to websites3, that hurdle is passed. Title III only applies to certain private entities. A judge would have to be convinced that SE is one of them, most plausibly a place of public gathering or place of public display or collection. In addition, the judge would need to be convinced that "the operations of [Stack Exchange] affect commerce", which shouldn't be too hard, since they show ads.
rjzii's answer deals with the practicalities of showing a violation is taking place, should it get past all the hurdles I've mentioned. It would probably take an actual instance of someone getting suspended or banned to show convincingly that SE is not making reasonable accommodations.
1: The Sixth, Ninth, and Eleventh2 Circuits
2: With some caveats that might not be applicable here.
3: The First and Seventh Circuits