There are two problems here. One is a lactose intolerance which is the loss of the enzyme required to digest lactose. All lactose is the same whatever the source. We are the only animal to drink milk out of infancy. So animals evolved with an enzyme, called lactase, to digest the sugar lactose. Animals stop making lactase after weaning because they don't need it anymore. In some human populations (those where milk was a major food source) we evolved to maintain the enzyme. Other human populations did not evolve this way because they didn't have a selective pressure to do so (they depended on other food stuffs). Pure genetics. You either lose the enzyme after weaning or you don't.

A casein allergy is different. In many infants, casein can be a problem to digest. But casein (unlike lactose) from one animal is different than that from another. Human casein is what humans evolved to digest. All bets are off when we put casein from other animals into us. For whatever reason, cow casein seems to be a particular problem. A casein intolerance generally manifests itself as crankiness and gassiness in an infant. This may not sound so bad to any non-parents out there, but when a child has trouble sleeping due to intestinal pain, it is not a trivial matter. This can often be hard to diagnose. And what many don't realize is that if a breastfeeding mother has cow's milk, it can also cause problems in the child.

My wife stopped eating milk products near the end of her pregnancy on the advice of her midwife. This was tough because cheese is a big favorite. Once Jacob was born we thought we were fine, and my wife started eating cheese again. My son reacted badly. Stop the cheese he would be less cranky and less gassy. Eat some cheese and he would get it through her milk and have problems.

My wife tried fake cheeses. They were horrible. Finally she found one that was barely tolerable. But then he acted up again! It was as if she had eaten regular cheese. Sure enough, when she checked the ingredients, THERE WAS CASEIN IN IT!

After weaning we kept Jacob on sheep's and goat's yogurt, soymilk, etc. No problems. Eventually most kids grow out of the cow casein problem. Kind of odd that people will gain the lactose intolerance but lose the casein intolerance. In my son's case he now drinks cow milk and eats cow cheese, though we often still use some soymilk and almond milk because he still likes it.

There are two food problems that can account for many problems in kids: casein and gluten. Gotta watch out for both. Most kids can be okay with both, but parents have to consider both if a kid is unusually fussy, gassy or throws up alot, has weight gain problems, or otherwise seems to have digestive problems. Gluten intolerance can be quite severe and is underdiagnosed. Fortunately Jacob doesn't have that (and we looked into it at one time).