The funniest thing about all this is just how badly some people want it to be that Joseph Rutherford had some association, as if it would imply something nefarious.
It is not at all established that Joseph Rutherford was the 'J. F. Rutherford' in some newspaper articles mentioning fraternal groups. And it's also possible that an otherwise prominent individual in a community could be invited as a guest speaker. (Though one of the articles touted as 'proof' has the J. F. Rutherford speaking "on behalf of the local Woodmen" rather than identifying him as a member of the Knights of Pythias. The same article says the gathering was represented by members from three states, so it is not unrealistic that a person could visit from Arkansas.)
But if Rutherford were a member of some fraternal group in the late 1800s, so what? It would not necessitate that he had any allegiance to the group later on. So why the rabid excitement about the possibility?