If I am not mistaken my CAA Cat1 med form asks for family history of all sorts of things (high blood press, heart disease etc etc).
I don't see why it is irrelevant, there are many conditions which are likely to be passed on. Why would you be any less likely to inherit some factor that makes you more susceptible to a heart attack than you are to inherit ginger hair or lack of height? Everyone seems to believe physical attributes that you can see - but ignores those you can't.
BUT, they are nothing more than another risk factor (history of heart disease in both parents would statistically increase the chances of you getting it. But then so does being overweight and smoking; if all three are present you have 3 risk factors - now much more likely than joe bloggs who has none but it is still nothing more than statistics; you won't have any issues until you DO have it)
Family history shouldn't prevent you getting a medical; just lets people know what to look for early. In some cases it may even save your life!!
Don't know about mental illness though - but I would imagine if you had a possibility of inheriting this you have done quite a lot of research already.