There are genetic predispositions and you are right everyone has mutant cells. However there are a lot of ways that people could be cautioned concerning the other causes which includes a number of things that make people uncomfortable.
As far as disease is concerned, I think if people know their family history or are aware of it, that could provide a huge understanding and awareness of what to expect. But also there are other factors that enter into the equation such as smoking, drinking, drugs (legal and illegal) and even ones own behavior plays a role such as diet, exercise, overall health and how risk taking ones job is etc. These are all things that must be considered.
Stress also plays a big role as well.