It is advised in the vEdAs that all should conduct the yajna karmAnushtAnAs and should wear the resulting 'hOma basmA' [*Ashes obtained from the hOma*]. That is why, initially, all
smArthAs did only basma dhAranam (smearing of the vibhUthi). Including those who worshipped Vishnu as their favorite deity. Even now, when yAgas are conducted, both
vaishnavaites and mAdhwAs have to wear the hOma basmA.
The practice of wearing 'nAmam' and in that, wearing with 'pAdham' and also with out it came in to vogue due to Vaishnava AchAryAs, who came later [*than Shankara*] is known from their guru parampara stories themselves, as retold by vaishnavAs. Later, when a separate religion and a sub sect were established based on Vishnu as the sole presiding deity, it became a necessity to give a new identity to the converts of this faith.
Similarly, 'gOpi chandhan' and 'chAndhu' were employed by mAdhwAs, when their new 'sampradhAyam' came into existence as a separate (social) group. For those, who didn't choose to follow any of these new faiths but continued to practice the original vEdic path as advocated by BhaghavadpAdhA, no new names such as vaishnavA or mAdhwA were given. The same old title, smArthAs, continued. Similarly, the practice - advocated by vEdAs from the very beginning and employed from generation to generation - of wearing vibhUthi (basma dhAranam) stayed back with smArthAs. A vEdic mantra for recitation exists, only for mixing vibhUthi with water and smearing.
Though a wrong impression that smArthAs are saivaites as they wear vibhUthi, has gained currency in present days, it can be said that, in reality the practice of vibhUthi dhAranam of smArthAs has got nothing to do with Shiva; but is based on its vEdic roots.
Before the establishment of vishistAdvaitam as a separate sampradhAyam by srI RamAnujar, even the vaidhIkAs who worshipped Vishnu with all devotion as their ishta dEvathA would have been smArthAs wearing only bhasmA. A SanyAsi does not have the right to conduct yajnas. Hence, he can not conduct a hOma and wear the resulting basmA. Even then, he will sport the vibhUthi.
During the 'pAncha rAthra dhIkshA', the vaishnavaites have to wear the hOma basmA, even today.
BhuddhA objected to the vEdic religion. He opposed yajnas and karmAnushtAnAs. He made no mention of IshvarA. Hence, there is neither (vEdic) karma nor bhakti in Bhudhism. During his days, smArthAs engaged in a lot of karmAnushtAnAs. If BhuddhA didn't speak of IshvarA, then, there was a section of followers of the path of (vEdic) karma, who believed, "What if IshvarA existed? Or what if He didn't? We have the karmAs enunciated in vEdAs. We'll have srEyas by simply practicing them". They are known as pUrva mImAmsakAs. They believed only in karmAs. Neither in bhakti nor in gyAna. They abhorred the principles of gyAna mArga such as contemplating the absolute truth continuously, doing Athma vichAra, becoming a sanyAsi by renouncing all karmAs and remaining always in the thoughts of Atman etc.