Korea's older population is conservative. Gay marriage isn't legal, 2015 was the first year gay pride wasn't shut down because of riots (there were still riots this year, but the police were on the pride parade's side this time) and it is much harder for younger people to be open about their sexuality.
Idols rarely (basically never) discuss serious issues, and LGBT rights is one of them. Below are two exceptions:
Jonghyun
In 2013, there was a movement called "안녕들 하십니까? 저는 안녕하지 못합니다." (How are you? I am not alright) when university students would write down their struggles and frustrations on bulletin boards.
One message, written by a transsexual university student who is bisexual, became Jonghyun's twitter profile picture. This of course caused a huge ruckus in the Kpop world, where idols don't usually express their opinions on important topics like LGBT rights. The fact that Jonghyun was so openly supporting this student's cry for equality was a really big (awesome!) deal.
In order to make sure the author of the bulletin board was okay with this, Jonghyun even reached out to them personally.
“I support you who are rightly exclaiming that difference is not wrong. I do not think you need comfort or concern. You are that strong. I hope health and warm is with you for this end of the year.” - Jonghyun
K.Will
Please Don't's music video's plot took the entire world by surprise with its twist ending. Through the whole video, we think that Seo In Guk is upset because the girl he loves is marrying his best friend. Turns out, we're wrong.
This is a subtle, artistic way of standing up for the gay community and it was beautifully done thanks to a great director, cast, and of course, musician.
Watch the music video on the card (slide left) :D
I don't have record of anyone saying things other than ignorant defensive comments like 'ew why would you think I'm gay man? *manly punch to the shoulder*" so I am not going to list those here.
Thinking about international pop music, with so many singers that are openly gay, singing about gay rights, etc - why don't idols ever mention controversial topics? Yes they're controlled by their agency, but come on!