The dairy rules for babies get confusing because different forms of dairy have different rules, and the reasons aren't always explained clearly. Here's the simple version:
Dairy as food (yogurt, cheese, butter, cooking ingredient): fine from 6 months.
Cow's milk as a primary drink: wait until 12 months.
The distinction has nothing to do with allergy and everything to do with nutrition. Cow's milk lacks the nutrient balance that babies need from their primary milk source. It's low in iron (and may actually reduce iron absorption), too high in protein and sodium for immature kidneys, and doesn't provide the essential fatty acids that breast milk and formula deliver. When a baby drinks cow's milk instead of breast milk or formula, they're getting a nutritionally inferior substitute.
But yogurt and cheese served as foods, in normal food-sized portions, aren't replacing breast milk or formula — they're complementing it. A few tablespoons of yogurt at lunch isn't the same as 24 ounces of cow's milk per day. The nutritional concern is about volume and replacement, not about dairy proteins themselves.