Saturated fats won't hurt you. Fats that will hurt you are any overly processed ones or tampered with ones. Avoid: Vegetable oils, canola oil, margarine, any sort of trans fat or deep fried fats. Also fats from animals raised with conventional farming methods.
Saturated fats from animals raised on grass without pesticides, hormones, antibiotics etc are all good.
People have been eating those sort of animal fats for a very, very long time. Instances of heart disease have increased with the introduction of wheat flour products and sugar and then increased further with the introduction of vegetable oils.