Early seasons of Supernatural were a lot heavier on the incestuous subtext than later seasons. I don't mean that Sam and Dean's relationship changed, exactly, but the framing of it shifted. They were put into fewer situations where the lines between familial and romantic or sexual got blurred. But I don't think this change was because anyone was concerned about how Sam and Dean's relationship was being perceived. I think it was because the show pivoted it's genre from gothic horror to paranormal fantasy.
Horror is all about transgression, and thrives in the space where what fascinates us and what repels us overlap. Gothic horror especially is grounded in melodrama and the taboo, and incest is a common theme. But the incestuous elements were never really about Sam and Dean's literal relationship, it was about the way that relationship felt - intense, alluring, profane.
As a horror story, Supernatural follows long established genre conventions when it threatens to dissolve the already weak boundaries in Sam and Dean's relationship. This works because it's taboo. That subtext is supposed to make us kind of uncomfortable. Maybe we don't recognise exactly what the subtext is implying and don't understand where the discomfort is coming from, but it evokes a visceral reaction anyway. And sometimes that reaction is complicated, because what's taboo can be disgusting or shameful or terrifying, but it can also be compelling or erotic or cathartic. Horror exists to explore these kinds of contradictions and to create a powerful emotional experience. The ambiguity of Sam and Dean's relationship plays into that.
Paranormal fantasy, on the other hand, has a slightly younger audience and the emotions it engages most are excitement and wonder. The kind of fear it uses is less often creeping dread and more an immediate thrill: think walking down a dark hallway vs a hand-to-hand fight. It's morality is supposed to be cleaner. It's characters have clear roles and easily defined relationships. So Sam and Dean can still sacrifice themselves for each other, but it's no longer framed as selfish or traumatic for the one left behind; the act becomes heroic instead. And when Dean murders the lover that Sam lied to him about, it's pragmatic and distant (Amy) rather than passionate and steeped in possessive jealousy (Ruby).
I love both genres but I think Supernatural was better as gothic horror. Later on, though it still plays with gothic elements sometimes, it also tries to impose clarity onto something that was intended to question more than it answered. To me, Sam and Dean were more interesting when the world of Supernatural leaned into the ambiguity and melodrama.