In this excellent answer
Swiftpushkar traces the concept to ancient scriptures.
it is said that
By the way, the story of Vishnu's incarnation Shankaranarayana is given in this passage from the Kuresha Vijayam, a 16th century account of Kurathalwan's debate in the court of the Shaivite Chola king:
In the puranic age, one staunch Vishnu baktha set his journey to Prostrate Sri Ranganatha. On his way he was completely exhausted and was terribly hungry. He found a temple nearby and decided to cook the food inside the temple and do the Aradhana to Perumal before consuming it. To his surprise, he found that to be a Shivalaya (Shiva temple). Being a true Vaishnava, his conscience did not allow him to cook there and he came out. But he fainted due to starvation. At that juncture, Sriman Narayana appeared in disguise in front of the baktha and offered help. The Baktha explained the he could not cook in Shivalaya. Lord Vishnu explained that it is not a Shiva temple but the deity inside is Vishnu. He then took the Baktha inside the sanctum and showed His true form with Sanka and Chakra as Vishnu is the antaryami of Shiva. Thus the Shankara Narayana Moorthy came to existence. This is only a leela performed by Lord with His baktha.
What is the position of the major Vaishnavite sects on the Haihara or Sankaranarayana concept?