Even then, there is an important reason for the prevalence of the general perception that advaitins are saivaites. After BhagavadpAdhAl, srI RamAnujAchAryA propagated vishistAdhvaitham.
srI RamAnujA was of the conviction that 'jIvan and Bhraman can not become one and be an advaitic reality. Even in the state of mOkshA, the jIvan remains as a different entity [*than the Bhraman*] and
realises that the very Bhraman itself exists as antaryAmi within him and also activates him. Even the Bhraman is not an attributeless and actionless 'nirguna vasthu', as advocated by Shankara. That
possessed virtuous attributes (sagunam). That engages in action too. The one that propells even the jIvan to engage in action is that [*Bhraman*] only'.
Till this, it remains only as a philosophical thought, applicable to devotees worshipping any [*vEdic*] deity. But, srI RamAnujA added here that,'Such a saguna Bhraman is MahA vishnu only; neither Shiva nor any other deity' and thus made vishistAdhvaitham acceptable only to those who held a particular deity, theologically, as their 'ishta dEvatA'.
Those who embraced the siddhAnthA of RamAnujA, till then, were smArthAs only. Even the vaidhIka matham or Hindu matham itself, till His [*srI RamAnujA's*] days, was only the smArtha matham. So, those who got converted to His siddhAnthA, which proclaims Vishu as the sole primordial Godhead, should have been from smArthAs only.
Some would have become His followers purely based on His philosophy. More than the philosophy, at the theological level, as the 'ishta dEvatA' of many - MahA vishnu - is established as the highest, many smArthAs would have opted for srI RamAnuja sampradhAyam.