The reason that Bhuvaraha, the Varaha deity in Srimushnam, is venerated by Musllims is that there was a Muslim feudal lord who was cured of cancer after praying to Bhuvaraha. Here is what this article from The Hindu says:
Here, it is pertinent to point out an interesting feature. Evidenced by relics and records, a Muslim feudal lord by name Syed Rahamathullah Suthari of Thaickal, near Killai, was suffering from a painful tumour on his back. On the advice of Killai Uppu Venkata Rao, a tahsildar, the Muslim lord prayed to Lord Bhuvaraha. The God appeared in his dream and he was rid of his ailment.
Also, the ruler who had been childless for long, was blessed with a child. Syed Rahamathullah Suthari donated 30 acres of land to Uppu Venkata Rao who built a mandapam at Killai.
On Masi Makam Day (February-March), Lord Bhuvaraha is carried on a palanquin from Srimushnam to Killai. At a place called Thaickal, near Killai, (which has a predominant Muslim population) the Lord is carried, to the accompaniment of music, through the streets, housing a mosque and a dargha of the late Syed Rahamathullah. In fact, the descendants of Syed Rahamathullah receive the Lord! The floral garland of the deity is laid on the dargha of the departed soul! At the dargha the Kazi recites from the Quran and prays for peace and prosperity of society. The Hindus also take part in this worship along with the descendants of Syed Rahamathullah. Thus the small sea-side village of Killai remains a shining example of communal harmony.
Another article from The Hindu provides more detail about how Muslims venerate the statue:
A speciality of the festival at Srimushnam is that the Chariot sports a Muslim flag, symbolising the Hindu-Muslim unity. In fact, every year in the Tamil month of Maasi, the utsava deity goes on a 20-day procession to Killai and other villages near Chidambaram. Another interesting feature is that the Muslims in the area offer prasadams to the Lord Yagyavaraha and in return they take the flowers of the Lord and offer it to Allah. The Muslim devotees are said to thank Allah for having brought Varaha Swamy to their place. The Bhoo Varaha Swamy temple in Srimushnum is the only temple that boasts of such a unity between Muslims and Hindus and this event continues to this day.