The anti-drunk-driving campaign of the 1980s was successful in large part because it joined the message about the dangers of drunk driving with a way people could avoid it, by introducing the concept of the designated driver, which ended up becoming a cultural norm. And this, it turns out, is central to the success of public health communication campaigns on topics like this one. Research has shown (here’s a meta-analysis on this topic if you want to read more) that fear is actually quite useful, the more the better. But the message also needs to increase people’s sense of efficacy, so that they have a way to resolve the fear through their actions. There are actually two kinds of efficacy that matter: self-efficacy, which is whether you believe you can successfully do whatever is being recommended (“Will I remember to bring a condom?”) and response efficacy, which is whether you believe the recommended action is going to work (“Do condoms prevent transmission of HIV?”).
If you succeed in making people afraid of something, like catching a terrible disease, they’ll look for a way to handle the threat. But if you don’t give them something they can do to alleviate the threat itself, they’ll deal just with the fear they’re feeling, by denying that they’re vulnerable (“That’ll never happen to me”) or just trying not to think about it.