What is the best way to support neurodivergent or otherwise sensitive employees who prefer to not be on camera, when cameras are required for specific meetings or work functions?

That is such a good question. From an HR perspective, I'd want to understand the value of being on camera. Is it critical to their role? Or are they using it as a proxy for engagement? 
Are there other ways to show they are engaged with the work instead? 

Additionally, in what ways do we mean sensitive? Could this be a form of accommodation?

First I’d be really curious to know what functions or duties are actually required to be on camera. 

I think the next thing is that you’re dealing with an ADA issue so can you prove this requirement outside of your organization as it’ll likely fall flat if the accommodation request is to not be on camera. 

Accommodations are on the rise and a part of the iterative process is working with the employee and physician to see how to aid them. I wouldn’t pigeonhole myself into a solution as that’s why there’s an interactive process for the employee. I think as a business you really need to look at your requirements, ADA compliance and accommodations process because you can get heavy lawsuits and fines for this. Especially if the solve is just to turn the camera off. It’s very hard for an employer to prove this solution would put the company in duress or burden them from what’s written here.