No comment about Chesterton's Fence but I have heard (but never confirmed!) one reason for left-handed stigma is to do with hygiene. The idea is that before modern hygienic standards (e.g. sinks with soap in every bathroom/kitchen), the left hand was reserved for "dirty work" (we are also considering a time before toilet paper...). So for example when you reach out to shake someone's hand, it would be rude to use the left.