According to 'Discover Neem'¹·: "Neem oil shampoo keeps fleas, ticks, mange mites and any other annoying biting insects away, and generally promotes a shiny coat and healthy problem free skin."
Neem oil shampoo is safe for cats, even for super sensitive, allergic-to-pretty-much-everything cats. In fact, you will probably find that the use of neem lowers your cat's sensitivity to environmental stresses significantly, and that its immune system in general improves.
Note: Some competitor's pet shampoos contain lavender essential oil. Lavender Essential Oil (EO), if ingested by a cat, can be mildly toxic.² ³ Where Lavender EO helps calm down dogs, it can do quite the opposite to cats. That's why Bridgewood Organics designs a formulation designed specifically for cats.
Ingredients: Purified Water, Ammonium Lauryl Sulfate, Ammonium Laureth Sulfate, Lauramide DEA, Lauryl Glucoside, Ammonium Xylene Sulfonate, Citric Acid, Propylene Glycol, Diazolidinyl Urea, Methylparaben, Propylparaben, Sodium Chloride, Aloe Vera Gel, Argan Oil, Avacado Oil, Coconut Oil, EDTA. Essential Oils: Neem Oil
¹ https://www.discoverneem.com/neem-oil-for-cats.html
² https://www.discoverneem.com/neem-oil-for-cats.html
³ https://www.felineliving.net/lavender-oil-safe-cats/