Cats are not allergic to sunflowers; sunflowers are considered non-toxic to cats. However, eating sunflowers may cause mild digestive upset such as vomiting or diarrhea, especially if consumed in large amounts. The seeds, especially with shells, can be a choking hazard or cause digestive irritation. Sunflower oil is also non-toxic but should be given sparingly to avoid digestive issues and weight gain. Overall, sunflowers are safe but should be kept out of reach to prevent your cat from eating too much.