You got me curious so I looked it up. NASA requires that astronauts be at least 62 inches (5'2", aka 1.57 meters.) So they already permit astronauts to be substantially shorter than average. They wouldn't take people with dwarfism I guess, or people without legs.
If I had to guess, these requirements exist because they need people who are compatible with existing equipment. For instance, astronauts on the ISS do not get personalized EVA suits; they pick one that fits from those which are already up there. Perhaps somebody without legs could fit in a suit with legs just fine (stuff the legs with some towels maybe, if the legs flopping around is a problem?) But for somebody with dwarfism or a related disorder, I can see this being a legitimate problem.
Incidentally, NASA also discriminates against the tall. For the Mercury program they wouldn't take anybody over 71 inches (5'11") and today they won't take anybody over 75 inches (6'3"). This doubtlessly is due to equipment that isn't sized for taller people.
I found the movie Gattaca to be a surprisingly good argument for this position despite being fiction and entertainment first and foremost.