I think it's a very difficult matter to judge and indeed I've not seen it so can't readily comment, however I don't think just because there is a piece of art whose subject matter is say rape, paedophilia, murder etc that it necessarily supports it, it may be very much the opposite, it may be a huge visual condemnation of it which makes people question their opinions which as a society we really should be doing on a daily basis, as people suffer these abuses everyday and only the adjustment of society and it's opinions can stop that, so no I don't have a problem per se with controversial works being on public display in fact I think it might do a lot of good.
With regard to the work you cite ( which I have not seen personally), when you say "young girl" how young are you actually talking about because if the depiction is of someone over the age of consent (16) then certainly it is not paedophilia, clearly if it is a child then that is a different matter. What is the artist trying to say in the piece?What is the context of it?
I have to say that trendy talentless art certainly isn't to my taste, nor are works that seeks to shock just for their own sake, however if the artist genuinely has something to say either personally or about society in general and it's well executed then I would support it, if not then they are just another attention seeking weirdo getting rich on the basis of other people's unhappiness.