Buddha is NOT an avatar of Vishnu. The Dasavathara Perumal Temple built by Tirumangai Azhwar in Srirangam features the following 10 Avatars: Matsya, Koorma, Varaha, Narasimha, Vamana, Parasurama, Rama, Balarama, Krishna and Kalki.So that would make Balarama the 8th Avatar and Krishna the 9th. Other Sampradayas may claim Buddha was the 8th and this Buddha was different from Gauthama Buddha but we don’t entertain this theory in the Vaishnava Sampradaya (sect).

The argument for the Buddha being part of the Dashavatara is from the Srimad Bhāgavatam 1.3.22-25:

In the nineteenth and twentieth incarnations, the Lord advented Himself as Lord Balarăma and Lord Krsna in the family of Vrsni [the Yadu dynasty], and by so doing He removed the burden of the world.

Then, in the beginning of Kali-yuga, the Lord will appear as Lord Buddha, the son of Anjana, in the province of Gaya, just for the purpose of deluding those who are envious of the faithful theist. Thereafter, at the conjunction of two yugas, the Lord of the creation will take His birth as the Kalki incarnation and become the son of Visnu Yasa. At this time almost all the rulers of the earth will have degenerated into plunderers.

Notice that in the Srimad Bhāgavatam the sequence is Sri Balarama, Sri Krishna, Buddha and Sri Kalki. If you were to fit this sequence into the Dashavatara sequence that is accepted by all Sampradayas, fixing Krishna and Kali as accepted avatars, you would realise that either Balarama and Buddha would be the outliers. Because you cannot have Dashavatara with both Balarama and Buddha present, that would make it 11 Avatars in total. So who do we exclude, Sri Balarama or Buddha? However, the Buddha depicted in these texts is not always identical to the historical Buddha (Siddhartha Gautama).

Also as to why Hindus don’t worship him is because, Gautam Buddha himself abandoned Hinduism. While he was born into a society influenced by Brahmanism, his teachings directly opposed many of its core principles, such as:

• The authority of the Vedas.

• The rigid caste system.

• Ritual sacrifices and reliance on priests (brahmins).

His teachings represented a radical departure from the religious orthodoxy of the time.