Yes. That is an experience we share with not just other disabilities but with minorities in general.
Physically disabled people often call it being a "supercrip"--the stereotype of the heroic disabled person who does amazing things. Many disabled people, both physically and cognitively, have to deal with this problem.
"John Henryism" refers to the same phenomenon in racial minorities, especially black people in America. They work too hard, get too stressed, and often shorten their own lives, just to try to be seen as equals.
Women who have full-time jobs, especially married women, often find themselves working two jobs--one being their day job, the other being as a homemaker. This is the result of having a career in a world where maintaining a household is still considered "women's work", and it can take a heavy toll on women who feel like they have to prove themselves as being equals in the workplace not just by being good workers but by also maintaining a model household to "prove" their competence.
It comes partly from not wanting to be restricted by the stereotype of incompetence associated with your minority status, and partly from buying into that same stereotype. Most people are presumed to be competent until they prove otherwise; for disabled people, it's the opposite, and we're presumed to be incompetent until we prove we aren't. Having to work harder than everyone else just to break even is a symptom of a society that does not accommodate for disability, nor see disabled people as equals. Hopefully, an awareness of this phenomenon will help us to be kinder to ourselves.