Yes, toothpaste interferes with fasting. Anyhting that even mimics food triggers your digestive system to think food is coming and then nothing. You want no energy wasted by the digestive system, which uses the most energy in your body.
Also toothpaste is all chemicals, your gums are full of blood capillaries and all chemicals get sucked in easily. That is why oil pulling works so well to get the toxins out. Oh! I am not suggesting oil pulling while fasting.