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I don't know much about Hinduism and the details of Indian history, but I feel that in India it is very common to nationalize foreign religions, beginning with the indianization of Sumerian deities, then with the indianization of Taoism that resulted in Buddhism, and then with the indianization of Islam which resulted in Sikhism. I thought this was hidden due to religious and nationalist issues but then I read that the Advaita Vedanta states that the same truth is described in different ways in all religions, that they all lead to the same end but were mixed with non-truth , and that therefore they must extract this truth present in all religions and mix with their own beliefs.

So my question is, this thought that all religions are true is shared in other Hindu schools? Do Indians openly adopt and syncretize foreign religions?