To preface this, I already know the abridged version of what all happens in the story, and I also know what the internet thinks of Ava. So I wanted to play it for myself and see if I can find these so called unforgivable sins the character does. I'm up to Eden-9 (rescue Jakobs planet, right after Maya gets merced), and I haven't really seen anything Ava does as offensively bad yet, and I feel everyone hasn't done anything out of character.
So essentially from what I've played so far, she hasn't really done anything deserving of hate yet.
I think the other thing is that on a series with a lot of hateable characters, she's not even fun to hate. The calypso twins were annoying as shit, gloating at your cutscene induced powerlessness, but they really worked that hate and drove it home with their streamer antics. Handsome Jack has his megalomaniacal bragging that gradually turns into a meltdown, to the point that killing him ends up being as much putting him out of his misery as getting revenge. Even claptrap, who I also want to throw off a fucking cliff, finds exciting new ways to be annoying, but Ava spends so much of the story being completely inactive that it's easy to forget she exists until she turns up to receive the rewards that you did all the fighting for.