I'm the exact reverse. The unaddressed conflicts in her character made me hate her both in the books I read (just the first 3, to be clear, then I stopped), and in the show (although far less in the show).
The death of her brother Viserys is always a sticking point for me. She did not care about him dying, for obvious reasons, although I found her almost complete lack of emotion, positive or negative, to that event, to be almost bovine in nature and terrible writing. But it was at that point that a light should have gone on saying 'My family name means nothing, because you can be a Targaryen prince/princess and still be a bad person and be brutally murdered by a horse-barbarian with no one to save you'. Instead her sense of entitlement is unaffected, and she even fucking names a dragon after Viserys! Whom she didn't give a single shit about! Why? Because he was a Targaryen, right? So he deserves respect. It's bizarre that she'd feel that way, having seen what she has seen.
The fact that she was treated like dirt and sympathized with servants and had lots of empathy should have pushed her beyond that stupid 'House' thinking. But it didn't, and she made very little sense to me because of it. Now that the conflicts are starting to bite her in the ass, and she's becoming more aware of them, I'm growing to like her more. What I really REALLY want to know is how she'd react if she was told what her father was like, and how the Targaryen name is seen by both the nobles and peasants of Westeros.