Yes, that was well put. I believe 'Hinduism' was a 'catch all' word invented by the British Raj to make life easier for themselves. I expect the main danger is when or if it becomes associated with nationalism.
The word 'Hindu' was given by the Persians sometime about 800 years ago to refer to people living beyond the river Indus. It referred to all the people living in India generally. The British started using it to refer to people who followed the Vedas (which is not true actually).....as different from Buddhism, Jainism and Sikhism. The word Hindu doesn't exist in any of our scriptures.
Hinduism then became a collective term to refer to a variety of beliefs and practices that existed in India....though with a common philosophy of karma, reincarnation and freedom. In fact most of today's Hinduism does not take anything from the Vedas. Most of it is from the Agamas, which are parallel non-vedic texts of the same period.
The word 'Hindu' has done a lot to unite the people of India. Without it how India would have looked today it is difficult to say.
