Interesting that this subject was raised while I was reading LIZZIE BRIGHT AND THE BUCKMINSTER BOY. Racism is central to the book, whereas in your story the MC's physical limitation may not be. Nevertheless, LIZZIE BRIGHT uses several techniques that may be useful models.
(1) Characters exhibit a range of attitudes towards race. Some take their opinion as "received truth," some doubt but conform, some change their opinion (one for a good reason--another for a bad reason), and the MC has never had to consider the issue before. So the outdated attitude is not monolithic, but shaded in many ways.
(2) The characters who exhibit outdated attitudes are already established as characters the MC finds dubious for other reasons. (It's not as simplistic as I'm making it sound--some of these people are the ones who change their minds during the course of the story.)
(3) Selected historically accurate words are used.
The only thing LIZZIE BRIGHT doesn't do is convince me that there is a real basis for the racist behavior (as opposed to racist attitudes). (The economic plight of the town is discussed, and the town elders are fearful, but nobody in town seems imminently threatened by poverty.) But maybe that would be too much moral ambiguity for MG?
As for your story, I can think of many convincing reasons why a "less than healthy" girl would be kept out of the marriage market in certain times and places. (Ideas that good, thoughtful people of that era would accept without question.) The assumption that she'd pass the problem on to her children, or be unable to bear children. The suspicion that the physical feebleness is a sign of mental--or spiritual--feebleness. The belief that she did--or was fated to do--something that deserved "punishment." Her need for extra servants, or her inability to do whatever work her station in life requires. The expectation that her condition would get worse, and she'd soon become a burden.