Considering I'm almost 6'4," that'd be pretty crazy for me to turn down any girl who is shorter than me. That'd be most girls lol.
As for how short I would date someone, I really don't have a specific height. In my opinion, it'd be silly to turn someone down strictly because of height. If height is the only thing "wrong" with a person, I would think that you got pretty lucky. Granted, height may influence the attractiveness of a person, which may affect the overall perception, but that is about it. I imagine under 5 feet tall is where things get kind of ehh for me. Short people can be cute haha.
As far as height goes, I think I'd be pretty turned off physically by someone substantially taller than me. I dunno why, I guess it is just how my mind works. Chalk it up to growing up and societal influence lol. My height and lower is fine.
I am 5'10", and I have no choice, but to date a women shorter, or as tall as I am. Women taller than me can get pretty intimidating. So there is my two cents over here just for you to answer your question.