I'm going to assume that the people who think peanut butter is bad for you are buying brands that are made using hydrogenated oils with lots of trans and saturated fats rather than unsaturated fats.
Saturated/trans fat, as well as too much fat circulating in your blood, can have severe impacts on the cardiovascular system, so yes they should be minimized. However, fats are still essential to cell regeneration (not just for energy, but also for rebuilding cellular membranes), so they are necessary, especially when doing exercise.
The reason why most people think fats are bad is because of a study done a few decades ago (can't remember which one) correlating body fat to cardiovascular diseases. So the assumption was people gained body fat primarily from eating too much fat. Even though health professionals suggested eating less fats, the American population still got fatter and less healthy (clearly there are other confounding factors, but I will just address one issue). More recent studies are claiming it is most likely due to higher fructose intake - I am isolating fructose because fructose is stored via a different biochemical pathway than glucose (fructose cannot be stored as glycogen, and follows a different pathway when converted to fat). Some of those byproducts of that pathway have detrimental effects on health - many studies link this to diabetes, hypertension, etc (I should stress that this isn't to say that fructose is the only cause). The fact that fructose is converted to fat isn't really the primary issue, it is how it is converted to fat.
Having said that, fructose isn't a "poison" as some want it to be labeled as. Fruits are full of sucrose (half glucose, half fructose) but also contain cellulose/dietary fibers that affect sugar absorption. Human physiology is much more complicated than what most people try to make it out to be.
I wouldn't recommended completely cutting out carbs (even a ketogenic-diet still has a minimum carb intake), as the brain is heavily/preferentially dependent on glucose as it's energy source, and to break down fat during the Krebs cycle, there needs to be a constant supply of oxaloacetate (which is a derivative of pyruvate - a carbohydrate). If you do go low-carb, then just make sure you're getting enough amino acids as amino acids can be converted to pyruvate to fuel the Krebs cycle (without either glycogen stores, carb or amino acid intake, this will come primarily from the amino acids in the proteins of your skeletal muscles). Also, note that the glycerol in triglycerides (how fat is stored) are not enough to constantly fuel the the Krebs cycle.
Finally, just as a reminder, even though the byproducts of converting fructose to fat, rather than the fat itself, is the primary issue with fructose intake - having high body fat/eating far over your metabolic needs still puts a lot of stress on your joints, vital organs, impairs physical function (flexibility, agility), affects kidney function, etc.
(and if I am mistaken/misinformed about something I just said, please let me know).