It puts at risk our status as fully human beings.
There's a young physician who has Treacher-Collins syndrome, where parts of the skull don't develop in the usual way. It's heritable, and in her family apparently started with her mother's father. The portrait of the three of them together is very instructive: his case of it was so slight that it went undiagnosed. Her mother's is much more noticeable, but apparently the penny didn't really drop for the family til Amie was born: she got stuck with the whole syndrome.
http://www.treachercollins.org/main.htmlOf course, some "disfigurements" that cost their victims their unconsidered social acceptance aren't really disfigurements at all: being Black, for example.
Perhaps the real disfigurement is in our brains?