BTS most definitely fits into my definition of K-pop, but in a hybrid manner.
They are idols — singing and dancing to the West-originated music, U.S. Black music in particular; following the Japanese idol sales strategies, like fan sign meetings and photo cards; and targeting the younger generation, mostly female. I said hybrid because they definitely tried to bring more authenticity via song-writing and the use of a hip-hop image, which idols usually lack and are therefore criticized for. Their early years were a struggle between seeking the approval of authentic music listeners as an idol group that does hip-hop. For now, they are just counted as a mega-K-pop group that embraces hip-hop influence and is not considered a serious, authentic hip-hop group. And I think this is because BTS is not involved in the K-hip-hop league, like by competing in Show Me The Money or befriending popular hip-hop musicians. And part of the reason they do not get along with the K-hip-hop scene is: one, BTS were ostracized from their debut and found no benefit from obtaining K-hip-hop’s approval anymore after they gained success; and two, K-hip-hop’s notoriety in not resolving misogyny issues would damage their reputation as an idol group that is mainly loved by female fans. It is not that BTS has never been criticized for misogynistic lyrics, but the opposite: a group of fans brought their problematic lyrics to public attention in 2016, and BTS apologized for the lines from their past works. Because of this history, they are in the position not to make the same type of mistake, which encourages them to cross-check their work with Women’s Studies experts when possible.
Big Bang went through a similar phase in the late 2000s and early 2010s. They were accepted as an authentic hip-hop group while maintaining their position as an idol boy band, which was quite uncommon. G-Dragon’s One of a Kind was an especially critically acclaimed record. And I have a theory that K-hip-hop’s acceptance of G-Dragon and Big Bang was because they share the language of . . . something that was inconsiderately imported from U.S. hip hop . . . which is . . . misogyny. It was not until 2016 that idol fans raised their voices about the misogyny issue (the first case was from BTS’s ARMY), but Big Bang had already gotten the reputation as a trans-idol group, and, in my opinion, part of the reason was the lyrics that objectify women, which made them look like they don’t comply with the female fanbase’s usual standards. YG was known to be a comparatively authentic Black music label since the 90s (1TYM, Jinu Sean, etc.), and that of course helped them to gain the reputation as well. (I also do agree that their production is close to U.S. Black music, thanks to Teddy’s musical genius.) YG recognized the benefit of K-hip-hop’s approval of authenticity in their music, so they consistently sent their trainees or idol rappers like MINO of Bobby to the Show Me The Money competitions and tried to win the title of “K-hip-hop approved idol rappers.” BTS chose not to go that way. They might have thought the approval of the West (which is counted to be superior to many K-hip-hop people) and ARMY was just enough for them.