How to refute the claim that the Buddha was an "avatar" of Vishnu? We as Buddhists know that Gautama Buddha didn't believe in a Supreme Being or an universal soul. We also know that the Buddha criticised the Vedic/Astik shastras, rejected the Vedic religion and the Astik school of thought, and challenged the hegemony of the Brahmans. But what about the people who claim that the Buddha was actually preaching the "Sanatan Dharma" as he was an "avatar" of Vishnu? 

The late S. Radhakrishnan, former President of India who was also a Brahman, claimed that the Buddha was actually preaching Hinduism:
"Famous Indian Hindu scholars like the ex-President of India the late S. Radhakrishnan stated: 'The Buddha did not feel that he was announcing a new religion. He was born, grew up, and died a Hindu. He was restating with a new emphasis the ancient ideals of the Indo-Aryan civilization'" (2500 Years of Buddhism, 1971, Government of India) 

While Babasaheb Dr Bhimrao Ambedkar, the Father of the Indian Constitution and one of the greatest Buddhist personalities of India, called this belief "sheer madness and false propaganda". 

Hence how do I refute this claim that Gautama Buddha was an incarnation of the hindoo deity Vishnu?
The easy way:

Ask for scriptural evidence for the claim. There is no reference in any Hindoo scripture as an evidence to this. 

The difficult way: 

Show that it is not possible using Buddhist ideas of Annata.

Easiest way:

Stay away from these arguments. I know where this is coming from. This is not disprovable or provable no matter how much you argue.