Yes there were cultural/academic differences and many different dialects of Hindi. Kabir sounds very different from Ghalib. But for the man on the street there was no difference. At most, you can argue that Urdu is the most popular dialect of Hindi. It wouldn't be correct, but less wrong.
Hyderabadi and Tamil Muslims speak a dialect of Hindi that they call urdu that would make Ghalib spin in his grave.
Differences within Urdu/Hindi are far more tremendous than the Hindi Urdu split. Calling them separate languages is crazy.
It's a cultural standard. Muslims call their language Urdu. Hindus call it Hindi. The language is the same, whatever you call it.
If you want to make your argument rigorous please give an estimate of pure textbook Hindi speakers (people who use avashya instead of zaroor, hriday instead of Dil outside academics and newspapers) and "hindustani" speakers.
My conservative estimate is less than 10M for "pure Hindi" and greater than 300M for regular hindi/Urdu.
This is because virtually every one from North India and Pakistan speaks the so called Hindi/Urdu mixed language. I have also met bhojpuri, awadhi, marwari speakers but I am yet to meet the mythical pure Hindi speaker and I am a really old guy.
What else makes a language? Syntax? Hindi and Urdu have almost identical syntax. There are more syntactical differences between Hindi and Punjabi than there are between Hindi and Urdu.
Moreover, there are hundreds of dialects of Hindi spoken in India, each with its own nuances and varying degrees of Urdu words.
In addition, there is no denying that Urdu and Hindi have some shared lineage.
Again will refer to the Wikipedia [0] for better coverage of this topic
[0] https://en.m.wikipedia.org/wiki/Hindi–Urdu_controversy