Milk & dairy — Food safety facts
Feed with care · Cats · full breakdown on the linked food page
Many adult pets are lactose-intolerant — milk often causes diarrhoea. Small amounts of plain yogurt are usually better tolerated.
Short answer
Most adult cats are lactose intolerant, so milk and large amounts of dairy usually cause stomach upset, gas or diarrhoea. A tiny taste is not toxic, but water is the best drink for cats. Cheese in small pieces is generally fine as a rare treat.