I would date a guy that is 5'6 or above ( basically 2" taller than me). Although I do have a preference for taller guys I wouldn't reject someone unless they were under 5'6, and even then the height would be a contributing factor l, not the only reason I would turn a guy down.
Ehh, as long as he's not a head shorter than me, it's fine. I've dated someone shorter and just found it awkward. But if it's only an inch or two, I could ignore it.