i would have thought more redheads by the litvish than the chassidish but that might be because of the circles that i run in . that being said I cant imagine that Sir Arthur Conan Doyle wrote The Red Headed League thinking about his chassidish neighbour
Well, from my mother's side I'm as Litvish as it gets.
im 0/3 redheads by my kids probably because my wife has dark black hair which is dominant . amongst my siblings 3/10 are gingy
My BIL (who's every hair in his body, including eyebrows, is bright orange) is 0/12 with his kids, though the next generation has one or two, but that might be because additional genes were introduced by his son-in-law.