Even then, the very identification of AchAryAl either as a saivaite or as a sAkthA or as a vaishnavaite, is nothing but viewing Him in a very narrow prespective. It is not correct to categorise Him, thus, as a bhakthA of a particular deity alone.
If it is asked as to why He has identified the saguna bhrahman as NArAyanA, in His bhAshya granthAs, it is because MahA Vishnu has been entrusted with the responsibility of lOka rakshanAm, during the
division of three primary activities. He has referred to the one who is incharge of protection [*of this creation*] as the very energy which takes care of this entire 'prapancham'.
AchAryAl is a saivaite and also a vaishnavaite and sAkthA too. We, the smArthAs also should be like that. The one who remains as a role-model for all smArthAs is srI Muthuswamy DhIkshidhar. He has viewed all the deities including even mAriamman , iyyanAr  and navagrahAs as the svarUpa of paramAathmA and worshipped all of them through [*His*] kIrthanAs.
The only paramAthmA, appearing as various deities is our objective. The attitude to view all of them with equanimity should be cultivated in us. Though, it is pointed out that even among advaitins, there existed vIra saivaities and vIra vaishnavaites, actually it [*such groupings*] is not in conformance with the manObhAva of AchAryAl and also with His advice/ instructions to us.
There is nothing wrong in having extra-oridnary devotion towards any particular ishta-dEvathA like Appaya dhIkshitA who remained a devout sAmbhavA (devotee of Siva) and LIlA sukar who was a devout bhAghavathA having deep love for Krishna, to quote a few from among advaitins. But, as these saints dissolved themselves in their bhakti for their ishta dEvathA without indulging in the 'nindhA' of other deities, we should also develop deep devotion towards our ishta mUrthy, without resorting to any criticism of any other deity.
This is one of cardinal principles of the vEdic religion known as smArthA matham. While denigrating the other deity, if one's dEvathA is claimed to be 'the' dEvathA, then it can not be considered to have the acceptance of vEdA. Going by this test, only we - the smArthAs, who follow the AchAryAl alone are 'pUrna vaidIkAs'.
I don't say thus. It is wrong, if I say so. It may appear as though I'm talking quite high of it, because it is my sampradhAyam. Therefore, this is not my opinion. It happened to be the opinion of three great personalities of yore.
Even the opinion of the mUla purushA of dvaithins, advaitins and vishistAdvaitins - vyAsa maharshi Himself- was this. In the anusAsana parvA of Bharatham, when He lists out the names of five mathams, that
were in existence from time immemorial, through BhIshma pithAmahar, He says,
sAnkhyam yOga: pAncha rAthram vEdhA: pAshupatham thathA:
In these, 'vEdhA:' is the vEdic religion; smArtha matham of later days. It contains arAdhana for all dEvathAs. The triad of karma- bhakthi- gyAna also is there [*in the vEdic religion*]. The school of thought which does the philosophical research, the SankhyA, is also a part of that. Even the yOga sAdhana is a part of vEdic dhAyanA. All these things do exist in the smArthA sampradhAyam also, which was rejuvenated by our AchAryAl.
In works such as SivAnandha lahari, Soundharya lahari and shatpathI sthOthram which is addressed towards srI MahA vishnU, even our advaitha AchAryAl has accepted dvaitA and vishistAdvaitha at different levels. In His 'yOga thArAvali', He has completely elaborated the nuances of Pathanjala yOga. Also, He has mentioned the twenty four 'thathvAs' of sAnkhyA, at many places, in His bhAshyAs.
: mAriamman is the (non-vEdic?) form of ambAl worshipped in Tamil Nadu. She is particularly known to protect devotees from small-pox. The most famous mAriamman temple is at Samayapuram,
a suburb of Trichy. Generally, non-bhramin priests known as 'pUjAris' offer worship to Her. Sacrificing goats etc is still a part of Her worship.
: IyyanAr is considered to be (again, the non-vEdic?) deity incharge of protecting the villages - Oork kAval dEivam in Tamil. He is seen to be seated on a horse with sickle/sword and His temples are always located beyond the village limits. Even He is worshipped by pUjAris with animal sacrifices.