I think Vedic Religion and Hindu Culture is more appropriate. Hindus by definition are people residing in the lands between Himalayas and the southern seas,ie,Arabian Sea,Bay of Bengal and Indidan Ocean. Correct me if I'am wrong but the word Hindu itself is formed of 'Hi' from 'Himalayas' and 'Indu' from 'Indu Sarovar' which means the Ocean where Indus river terminates. This would imply that irrespective of religion,anybody staying in those lands is 'Hindu'. So saying Indian Muslims,Indian Christians etc is not correct.

Running is the best thing God ever created!
- Rabbit