Ultimately, the point is that it makes very little sense to project Shaivite-Vaishnavite sectarianism - which in its virulent form doesn't go much further back than the period of the Imperial Cholas - onto Adi Shankaracharya. It's about as absurd as trying to interpret the rivalry between the Cholas and Pandiyas in the light of DMK-AIADMK rivalry. Shankaracharya was not a sectarian Shaivite or a sectarian Vaishnavite, because sectarian Shaivism and Vaishnavism did not exist in his day, thank God.