I think the way Buddha thought people should have the freedom to practice the religion of their choice in peace, Do No Harm.

The name given to the vast and diverse groups of people in India is a recent construct that covers 100s of different Gods and deities and India was made up of thousands of small and large kingdoms and cultures. The state of Nepal, which didn't exist at the time Buddha was born claims the small town on its border with Northern India called Lumbini is Gautama Buddha's birthplace.

Buddha was said to have been born in the gardens of Lumbini. At that time the area was a conglomerate of clans which were organized as a republic. Buddha was born during a time of conflict, warring clans and peaceful clans that formed alliances with each other. Buddha's father was the warrior king (kshatriya varna) of the Shakya clan which was conquered by a neighboring clan after Gautama became Buddha.

Time to push back the Buddha's birth date a century or so? Archaeologists may have uncovered evidence of the oldest Buddhist shrine yet discovered, dating to around 550 B.C.,

The word Hindu is derived from the Sanskrit word Sindhu which is the local name for the Indus River that flows through the north-western part of the Indian subcontinent. Sindhu also means sea. The word Hindu or Indu was used by Greeks to denote the country and people living beyond the Indus river.,

The Shakya Clan in India: A Rediscovered Heritage,

Family of Gautama Buddha

The division of northern India into republics and kingdoms continued into the time of Shakyamuni Buddha (566–485 BCE). The major ones were the Vrji Republic, with public assemblies and democratic institutions, and the autocratic kingdoms of Kosala and Magadha. Both types of state, however, functioned within the ritual structure of Brahmanism. This is because Brahmanism described the duties of a ruler, rather than his powers and form of government. Buddha was born in Shakya, a former republic incorporated into the Kingdom of Kosala, and taught in both Kosala and Maghadha, as well as in the Vrji Republic.