this is a good question! okay a bit spoiler ahead so skip this if you don't want to know. his parents are aware that he's not straight, and they also know about his lifestyle (partying, hookups, and all). his father, being in the film/entertainment industry, is pretty much familiar with the culture. that's why the siblings sarcastically said that he's "open-minded". his father isn’t openly accepting or entirely against sunghoon’s sexuality, he sees it as a phase—just sunghoon being young, stupid, and "exploring" things, something he believes sunghoon will grow out of. he also knows sunghoon fears him and how much control he has over sunghoon so in his head he thinks it'd be easy to slap him back into heterosexuality if needed, for the lack of better words LMAO. lastly, the marriage of convenience to elevate status idea is not really relevant here because their family isn't exactly rich RICH for marriage "politics" to be a major concern