It's seen as a formal license to spread any specific group-on-group antagonism to all members of the associated formal class/caste. All aristocrats/capitalists/cool people are entitled condescending parasites, all serfs/poor workers/uncool people are dull, crude and amoral; all Jews/Anglo-Saxons/Irish/Slavs/Blacks/Westerners/Catholics/Hugenots/heretics...
My model is, divides along official or semi-official lines in society have practically always tended to accumulate resentment in "quiet" times and blow up in a crisis. Just imagine how much more peaceful and nicer South Africa would've been today, if the goddamn Afrikaners could've got along with colored people like the British did in India! And you'd add a new faultline just for some tactical gain?
The comparison of India to Africa isn't valid because the starting conditions are sufficiently different. Also note that the question is somewhat rhetorical. We de facto do have several kinds of citizen. Can you think of which kinds?
To provide a counter point the Ottoman Millet system seems to have worked pretty well at keeping the peace in that state. Also India is a bad example for your argument for another reason, recall some of the biggest problems the British had there was when they tried to abolish or weaken or even just ignore the traditional caste system.
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.