It all depends on the type of keto diet, rez. On a CKD it's a good idea to minimize carbs until your carb-up. Some people say less than 30 grams per day, others say as close to zero as possible. If you're on an Atkin's style keto diet (no carb-ups) then cheese is OK as long as it fits into your daily allowance of carbs. But even Atkin's recommends you get as many of your carbs as possible from fibrous veggies. All cheeses have carbs, it's just a matter of quantity. If you're not on a keto diet, then the advice to reduce or eliminate milk is for similar reasons. You can lose fat with milk in your diet, but it is still a good idea to get most of your carbs from fibrous veggies or whole grains/beans IMHO.
The guy that one the National open title in my country (2 years ago now) was still drinking 6 liters of non-fat milk per day until 2 weeks out from competition. But he was on a huge amount of gear and was a very experienced and controlled dieter (and a walking chemist LOL). So milk, per se, is not bad if you're not allergic to it. But it is calories and it includes carbs so that has to be taken into account.
The guy that one the National open title in my country (2 years ago now) was still drinking 6 liters of non-fat milk per day until 2 weeks out from competition. But he was on a huge amount of gear and was a very experienced and controlled dieter (and a walking chemist LOL). So milk, per se, is not bad if you're not allergic to it. But it is calories and it includes carbs so that has to be taken into account.