Fine in theory but not really reality.
In a practical sense people will have expectations about what the service on offer entails, and I would think most parents would assume in the kids section of the library the books would not really be adult orientated. I don't think any parent is going to go and read every book it contains before giving their child access to the library.
There are loads of cases where peoples trust has been abused, the creche furore in Dublin, the exposure of shit that went down in some old folks homes, basically people did not know this and thus were outraged when it came to light simply because they put their trust and indeed had no choice but to put their trust in both these cases because it would have been impractical and probably impossible to sit in on the creche all day long or similarly spend an inordinate amount of time in the homes before they placed their elderly parents at their mercy.
And re the above book I would think there are a shitload of parents who have no idea that book is shelved in the childs section, some who may have no problem with it, but I'd imagine quite a lot who would have a huge problem with it, so it is not necessarily the decision of the parent if they are unaware of the contents of the library based on what would be a natural assumption, namely the kids section contains kids books.
I'd agree with Dan on his premise of the library having a duty of care to kids, the same as the school you send your kids to, the GAA, Rugby or whatever sports clubs your kids may attend also have a duty of care to them.