Well as far as I remember early historic fiction from pre modern China the Shaolin and the Wu-dang fell out when the Shaolin continued to resist the Manchu even after it was clear it was over. This seems to have been exasperated over a killing at a dye works by a Manchu backed Wu-dang student who then entered Shaolin and after training got revenge. This seems to have lead to tit for tat killings.
This was in the late Qing Dynasty martial arts novel Evergreen I think. It was written shortly after the events and is based on some facts I think.
This is a discussion on it.
http://home.planet.nl/~padbe017/Nan_Shaolin_6.htmThe history of the Pak Mei style also links Wu-dang to the Shaolin temples burning although indirectly.