The term "Hindu" was never used as a self-identifier before 1800s. People identified themselves by sect (e.g., Shaivites), or caste. So the terms Hindu/Hinduism have no history. To say Hindu/Hinduism was opposed by Buddhism/Jainism 2000 years ago is ahistorical.
What Buddhists, Jains, Lingayats, etc. opposed was Vaidik brahminism. "Hindu" was an outsider label to those who lived beyond Sindhu R. Using it as a relgious identity label to pre-1800 peoples is problematic. It forces our ancestors to belong to a religion that never existed.