It's true in places you mentioned from even my understanding from multiple people. But it's the same in the whole of India is not correct, as Kerala comparatively has very less problems like this. It's actually surprising for people from Kerala to even know such issues still exist even in metro cities of other states. True that it makes sense to generalize your comment as Kerala is just 2.5 - 2.7% of the Indian population.
Trying to get a house in Delhi as a single, straight male is an exercise in discrimination 101. Landlords will ask you if you drink alcohol, eat meat, have female friends, belong to a non-Hindu religion (especially if you're muslim), your caste, and heck, even what city/state you're from.
My friends have been denied housing simply for being from a state with a somewhat poor reputation. Some were denied because they were lawyers AND from a specific caste (the landlords feared that my friends would somehow take over the property through legal shenanigans). And I won't even get into how hard it is for a muslim male to find housing in India, especially outside of big cities.
So much of this simply never gets talked about in Indian society. But its just accepted as something that happens. Sometimes feel that we're developing backwards as a society.