What happens when you mix milk and coke?
The phosphoric acid causes denaturation of milk proteins which precipitate out of the solution (milk is an emulsion, to be exact). The flock that is formed also adsorbs dye molecules (caramel) which is why the solution become clear.

There is nothing coke-specific about it. Any acid would denature milk just like that. And nearly any huge organic molecule would get absorbed, just like caramel dye.