[senkora]

This is called being a “universalizing” religion.

The big three universalizing religions are Christianity, Islam, and Buddhism.

You can understand a lot of religious history as just those three religions expanding and displacing other belief systems.

Contrast with non-universalizing religions like Judaism, Hinduism, and Shinto.

[larksimian]

Hinduism is hardly non-proselytising. After all there's not a lot of Buddhists left in India. The Brahmin caste pretty intentionally and comprehensively reacted to and pushed out Buddhist practices once they became threatened by them.