I feel like questioning their competency would absolutely be a thing. I have pretty severe ADHD, and I know that even when properly medicated I still have some traits associated with it that could possibly give me a hard time.

I think it might be tied to them if made public, but wouldn’t necessarily make them unelectable as far as ADHD goes, the others you mentioned might pose a problem though.

With Bipolar, even properly medicated people will still have some issues that make it hard to execute their office. Manic episodes can make people have public outbursts even when managed and that can be manipulated.

For Asperger’s/very mild autism it probably wouldn’t be a problem. As long as the person in question has been diligent in learning things like social cues. For OCD I don’t think it would be an issue either unless they haven’t gotten proper therapy and are prone to tantrums.