I have no problem with characters being polyamorous, hell I wouldn't even mind if Brienne was polyamorous. The problem only arises when the game gives the player no choice but to engage with the content (or they do have a choice but said choices either suck or are irrelevant) or makes the PC feel like third wheel when they do engage.
Ironically it's why people hate Cait, cause although you're given a massive disclaimer on what the character is about, and are given the option to say no, the player is still forced or at least heavily pushed towards her character. She's constantly shoved in your face and there is no option to tell her to fuck off.
Azzyran and Liaden refuse to involve the player in their relationship, especially if the PC is male, which sucks and renders that particular slice of content worthless to me. On its own its something worth being annoyed at but not outright pissed about (Keywords: "on it's own"). The inability for PC participation is bad enough, but then Azzyran just won't fucking shut up about Liaden. She'll tell you how Liaden means the entire world to her, and then she'll turn to and be like "oh, your still here? your fine too I guess" which is, as you could imagine, a tad fucking insulting. And then there's the Dawnsword quest, which makes Azzyran the most punchable companion in the entire game, second to Quin of course. Azzyran being poly isn't inherently a bad thing, and I'm willing to overlook content that doesn't involve the PC if it's optional to engage, but sacrificing the player for the sake of uplifting a character that exists solely to fuck your girlfriend is going to piss people off, regardless of how polyamorous they are. Combining all three is just asking for a disaster.
As for Atugia, she has incredibly inconsistent writing, and is generally Schizophrenic in all her depictions, but as far as i'm concerned, all of her threesome/NPCxNPC scenes are optional, and she doesn't go on a tirade about how much better Arona's dick is than yours every passing hour of the day. Until the writer finally gets a grip on how to write this character, she's neutral to below average in my books.