based on the red color of the flower of the ginger plant. Things that were red got described as ginger. There are some obtuse references in print that date to the mid-1800's of calling a rooster ginger-colored, or a man's moustache ginger.

But for the US, it is likely safe to say the term comes from the Gilligan's Island character. Granted, she was likely named Ginger in the first place as a nod to her red hair by someone who was aware of the British slang. But it didn't enter the US vocabulary until people who grew up on Gilligan's Island started having the Mary Anne vs Ginger debate while drinking...which is really a euphemism for brunettes vs redheads.