Austroasiatic influence on India

«Indian culture itself arose from various distinct cultures and peoples, also including Austroasiatic linguistic influence onto early Indians. However some scholars, such as Professor Przyluski, Jules Bloch, and Lévi, concluded that not only linguistic but there are also some cultural, and even political Austroasiatic influence on early Indian culture and traditions. India is seen as a melting pot of western, eastern and indigenous traditions. This distinctly Indian cultural system was later adopted and assimilated into the indigenous social construct and statehood of Southeast Asian regional polity, which rulers gained power and stability, transforming small chieftains into regional powers».

I wonder how strong was the Austroasiatic influence on Indian culture and Hinduism? I have also heard that the Shakya tribe, from which Buddha Shakyamuni came, may be of Mundian origin. Is it possible that Buddhism was formed under very strong Austroasiatic influence?