I've noticed more and more seemingly harmless food items are now carrying warning labels saying they may be carcinogenic or expose consumers to carcinogens. the latest is blackstrap molasses. do we need to avoid these food items or are they safe?

Not the food itself but the method for making and preserving that food and one common example is green tea which can be contaminated with carcinogen(s) during production in certain countries.

There is a risk and benefit in most situations. You can reduce your risk of cancer by adopting healthy habits: Eat a mostly vegetarian diet, avoid alcohol, tobacco and street drugs, avoid excessive exposure to sun, maintain healthy weight, get HPV vaccine, exercise 30 minutes each day, drink enough water so your urine is mostly colorless. Wish you good health!