It's become meaningless.
Like 'I have anxiety so can't do x, y or z' or seen often on MN ' please be kind/gentle, I have anxiety'.
It's designed to shut people down and make them back off. Literally everyone has anxiety. Anxiety is a really normal thing.
Anxiety disorders however are different, and having had 2 for decades and ADHD and also working in mental health services, there's a huge difference.
It's normal to be anxious about meeting new people, or to be anxious about any other new life situation. or to be anxious about an essay or an exam.
As a supervisor now i'm the one like you, pissing people off by asking for evidence or at least an explanation and a discussion about what can be put in place to improve things or make reasonable adjustments - the emphasis being on reasonable.
A lot of people seem to think they can just say mental health/anxiety/ADHD/ND and their employers or supervisors have to say 'oh sorry, won't bother you again' because so many employers and supervisors are scared by the terms and worried about being accused of discrimination.
If you can't get meet all the requirements of a course or a job and won't even discuss reasonable adjustments or make requests that are unreasonable then you can't finish that course or work in that job. And it isn't discriminatory.