Are low carb high fat diets safe?

Safe but not healthy. Low carb is good especially low refined carbs but high fat is not good especially animal fats. Beware of foods that come from animals that walk on 4 legs (or that are mistreated!) eat lots of fruit vegetables grains high quality protein. If you are diabetic watch out for the fruit. There are a lot of very good websites that can advise you on healthy diets. And don't forget to be active!