While I agree with you factually that the term hasn't been officially around since before 16th century but it definitely was used before the British arrived and

While I agree with you factually that the term hasn't been officially around since before 16th century but it definitely was used before the British arrived and colonised India for good https://www.britannica.com/topic/Hinduism#ref261605 https://www.britannica.com/topic/Hinduism#ref261605. Besides, let's just be honest - today Hinduism/Hindu is a religion - there is no two way about it - practically and technically! This reasoning, that "oh, it's just a way of life", is often provided by people who try to deflect the argument away from Hindu nationalism, extremism, and fanaticism - especially of today. (This might not be your intention though).