I don’t know where people like you get their ideas about medieval times, but even if you confine your view to a fairly narrow part of history and the world you’re still wrong… Disability was a huge part of life as one would imagine of a relatively violent and hard world with little medical technology. Blindness, deafness, muteness, lameness, mental illness and physical deformity were all facts of life then as they are today even if the causes and treatments were not as understood. Varying degrees and types of what would now be called disabilities were very common among the peasantry and less common but much better cared for among the wealthy.
While of course there is a storied history of monasteries sheltering the sick and disabled and of leper colonies, most people with disabilities in medieval Europe lived within the community, working where they could and being supported and cared for by their community and families where they couldn’t. Begging obviously was where some ended up but was not the default.