The question asks whether it is OK, not whether they should do it or not or whether it would be betraying B - who they may not even know.
It's morally reprehensible, making it wrong however you paint itNo-one is saying C is worse than A if something happens, but they are not absolved of any wrongdoing.
Perhaps I wasn't clear.
I was basically saying that, from my point of view, it's not a moral issue on C's head. They aren't wrecking the relationship: they're a symptom not the cause.