We talk about that stuff just fine now (at 4), but I remember DD being pretty disturbed by it a while back. DD has sort of the opposite reaction, though, which is that when she worries about something she wants to talk about it, even more than I think is advisable.
Things that might help:
When talking about bad or scary things, I often use the phrase "the bad thing is." When she starts feeling scared, DD will stop me and ask for "the good thing." So, for example, if we were talking about strangers, I might say, "The bad thing is that sometimes people aren't friendly even if they look friendly and might do mean things." Then, the good thing is that if I am with her, I will keep her safe. Or the good thing could be that most people are friendly. Or the good thing could be that when the police find those people, they put them in jail to stop them from hurting anyone. Etc., etc.
DD loves books about jobs. We've read a few about firefighters and police officers. I think that the perspective of someone whose job it is to help people is a less scary way to talk about situations in which people need help. A book about firefighters triggered a lot of discussion about what we would do if we were in a fire, and how we could avoid getting in a fire, etc. A book about police officers DD read recently included the officer finding a child who was lost and helping him get home; it was totally not scary because the story starts with him being found. But we were still able to use it to talk about what DD would do if she were ever lost.
