Solution 1:

My 1972 reprint of “Passing English of the Victorian Era” by J. Redding Vale, first published 1909, has this definition of butcher, as used in public houses:

One of the synonyms for ‘stout’ - obtained probably from the general observation that few butchers are thin and narrow.

If then butch comes from butcher, then it was more to do with corpulence than rugged masculinity.