If you are talking about they whole makeup thing. Trouble is I think of male K-pop idols as very masculine and therein lies the cultural conflict. So to answer the real question my favorite idol that I actually consider to be androgynous is Amber of f x.
10 Best Androgynous K-Pop Idols That Will Blow Your Mind Away HeeChul.
There is one group however that is challenging gender roles with their music and concept. Most K-Pop groups classify themselves as either male or female idol groups. Even surpassing popular female idols eventually. You may think that they look like girls but Im going to see if I can change your mind.