The fact that there are people preying on children over the internet is disturbing, but I don't find it surprising. I'm not upset in the visceral sense because I can't keep that feeling up for something that has been a matter of fact about the world since time immemorial.
The way people engage ethical questions is very complex. One way of looking at this is along the emotion vs. logic spectrum. Both strategies work, but have different advantages and require different feedback loops to improve. But it is our collective responsibility to engage those feedback loops as much as possible (which you're doing by your posting, which I think took courage).
On this particular issue it seems you're more towards the logic end. That's fine. If that makes you uncomfortable, that's ok. Dig a little but don't judge yourself - this only hurts the process.
At the end of the day, in the words of Batman: "It's not who you are that defines you, it's what you do."
Edit, for anecdata: I lost a parent to disease early in life, and it took me years to come to terms with the fact that I very rarely feel any emotion about it. Interestingly, I find my reaction changed with age.
I'm not that worried either. This issue is already being discussed quite widely, children will get educated, etc.
Naked/sexual images aspect doesn't disturb me much, what disturbs me is the manipulation/secrecy/blackmail aspect, and attempts at real life contact. Both is hopefully preventible with educating children on how to treat the internet, and how to keep their privacy, and how to recognize danger and deal with it. Newer generations of parents will have more clue about this, and will be able to prepare their children for this better.
From what I've heard so far about the issue, and given how widespread this is, I have a theory that children get targeted more, simply because they are more likely to give attention to people giving them some attention and simple adoration.
There are an infinite number of things in the world that are troublesome, that don't affect you. You do not want to let it take over your life. I have a friend with severe anxiety and he worries over everything that doesn't involve him or that is inconsequential. He is absolutely miserable because of it. You do not want to be like that.
That said, I feel anything to do with children being victims much more viscerally now as a parent than I did before.