A lot of studies are showing the largest factor in heart disease and obesity is not fat, but carbohydrates (specifically starches and sugars, not dietary fiber or sugar alcohols).
A lot of people today still think Adkins died of heart disease because of a (later rededicated) Reuters article with bad information (he was old, slipped on a piece of ice and bused his skull). I wonder had the Adkins diet movement not died off, if we'd see a significant reduction in obesity today.
It might be difficult to eat vegan, but it's much more difficult to eat low carb. Look carefully at everything in your pantry.