Today is Buddha Purnima. It is also the Birthday of my mother. She was named করুণা, Karuṇā by her mother, meaning compassion, a virtue that Buddha stood for. I like it. A very subtle reference to the Lord without being obvious.
At a later part of her life she worshiped the Buddha, but she was not a Buddhist. She believed Buddha to be the avatar of Vishnu in Hinduism. Buddha has been depicted in Hindu scriptures as a compassionate teacher who preached the path of ahimsa, non-violence.
Buddha is described in important Hindu scriptures, including almost all the major puranas., However, some occurrences of 'Buddha' simply mean 'a person possessing buddhi', most of them, however, refer specifically to the founder of Buddhism. In the Puranic texts, he is mentioned as one of the ten Avatars of Vishnu, usually as the ninth one. Another important scripture that mentions him as an avatar is Parashara's Brihat Parashara Hora Shastra.
Buddha is often described as a yogi or yogācārya and as a sannyāsi. While in a few places Buddha is described as beautiful, devasundararūpa, of yellow skin, and wearing brown-red or red robes.
In the Bhagavata Purana, Buddha is said to have taken birth to restore the devas to power:
kalau sampravṛtte sammohāya sura-dviṣām ।
buddho nāmnāñjana-sutaḥ kīkaṭeṣu bhaviṣyati ॥
— srimad-bhagavatam, 1.3.24
In many puranas, the Buddha is described as an incarnation of Vishnu who incarnated in order to bring either demons or mankind close to the Vedic dharma.
The Bhavishya Purana contains the following:
At this time, reminded of the Kali Age, the god Vishnu became born as Gautama, the Shakyamuni, and taught the Buddhist dharma for ten years. Then Shuddodana ruled for twenty years, and Shakyasimha for twenty. At the first stage of the Kali Age, the path of the Vedas was destroyed, and all men became Buddhists.
Before the eighth century, the Buddha was accorded the position of universal deity and ceremonies by which a king attained to imperial status were elaborate donative ceremonies entailing gifts to Buddhist monks and the installation of a symbolic Buddha in a stupa. This pattern changed in the eighth century. The Buddha was replaced as the supreme, imperial deity by one of the Hindu gods, except under the Palas of eastern India, the Buddha's homeland.
Previously Buddha had been accorded imperial-style worship or puja. Now as one of the Hindu gods replaced the Buddha at the imperial centre and pinnacle of the Cosmo-political system, the image or symbol of the Hindu god came to be housed in a monumental temple and given increasingly elaborate imperial-style puja worship.
Other prominent modern proponents of Hinduism, such as Sarvepalli Radhakrishnan and Swami Vivekananda, consider the Buddha as an example of the same universal truth that underlies religions.
A number of revolutionary figures in modern Hinduism, including Mahatma Gandhi, have been inspired by the life and teachings of the Buddha and many of his attempted reforms.
To my mind, Hindu worship of Buddhism is part of an effort, itself a reaction to Christian proselytizing efforts in India to show that "all religions are one", and that Hinduism is uniquely valuable because it alone recognizes this fact.
The main reason why Buddhism is so very popular outside India and so very rare in its birthplace India is due to the fact that Buddha is NOT considered outside Hinduism. Most Hindus worship Buddha as an Avatar of Vishnu.