Khan was a warlord, but he was well regarded by his own people, and not dumb (at least tactically). I imagine given the morals of the age, that he would make no secret that he and his men take "war brides", since that sort of thing would be too hard to keep secret once a million babies are born from it. Better to normalize the practice and act as if nothing is wrong. If you pretend so with enough dedication, if you're respected, people will assume THEIR viewpoint is the flawed one, not yours, and adjust their worldview to match.

It's like the statement "people die in war". If you break it down, it's a HORRIFYING statement. Death is a terrifying, terrible thing. But the rulers go "fact of life, war means death, now soldiers go march, kill them and die yourselves too." and they go "seems about right.". When the rulers said "of course we take war slaves", the Greeks, Romans, many African nations, they all went "yup, war slaves makes sense, the rulers say so". I don't see it being any different with "war brides".