Being a fan of someone means that you'll inevitably like someone who does offensive things, but the important thing is not to cover up the mistake, brush it off or excuse it as something small. The only way someone can learn from their mistakes is if they realize what the mistake is. However, I understand that most of these groups do not have any or little control over their concept, what they get to wear and so forth because their company is the one who makes all the decisions, but calling the group out for their mistake will force the company to acknowledge what they did.
There's a big issue with colorism in the Korean pop industry and in Asia in general. I think that deserves an article all by itself, but saying that it's just "culture" is simply a lazy excuse that further perpetuates stereotypes and discrimination.
With that being said, here's a list of problematic things your faves have done.
1. G-Dragon Glorifies Maikol
Maikol is a character from a famous Korean cartoon called Dooly. Maikol a blackface character "based" off of Michael Jackson.
2. G-Dragon Portrays Blackface
Blackface is not okay and has a long racist history behind it. In 2013, when G-Dragon posted the Instagram photo below, controversies and criticisms erupted from the public.
Here's another.
3. T-ara's 2010 Release Of "YaYaYa"
Need I say more? Read here for more about T-ara's "YaYaYa" and about cultural appropriation in the K-Pop industry.
4. Luhan Says "Lighter Tone Skin Is Better"
He also tells Tao that his skin is nice, but "the only problem is the skin tone."
5. Cornrow Appropriation In General
Although to give the artists some credit, I don't believe they had much choice in their hairstyle since their companies would be the ones pushing a style/concept onto them. Taylore from Seoul Beats goes more into detail about the appropriation of cornrows in 4Minute's Crazy concept and in the K-Pop industry in general.
6. Rap Monster "Talks Black"
In 2013, BTS went on a Korean radio show called Shim Shim Ta Pa and when asked to show their talents, Rap Monster said that his talent was "talking like a black person."
7. 2NE1 "Transformed Into African Ethnic Girls"
Allkpop.com called it "so chic." See what an actual African of Igbo descent thought about the photo shoot.