I think that if we banned all the books that offended someone there'd be no books! I suspect authors write books knowing that some parts of them might generate a reaction - intentionally or otherwise.
My own background means there is almost nothing that offends me, though that doesn't mean there aren't things I don't disagree with.
In terms of dd, we have always been very clear with dd deciding what she's comfortable with. When she was very little and we read to her, if she asked us to stop a book we'd talk about why and either keep going if the issue was resolved or stop it all together. We re-try those things she finds confronting every now and again (she wasn't ready for Harry Potter when we first tried them, now she's on the 6th book). Now dd censors her own reading and will put aside anything she finds she is uncomfortable with. Having said that, I wouldn't bring books home from the library for dd that had significant violence, abuse, sex etc. But mostly because she just has no context for those things at 6 and so they'd be confusing and probably a bit scary.
If there are topics I disagree with in things dd is reading, I will always raise them with her.For example I have big issues with the portrayal of girls in lots of books (playing into gender stereo types) and so we talk those things through and I explain my point of view. I don't strop her reading them though.
Ultimately, like others have said, I feel like being exposed to different points of view is extraordinarily important.
