Below is an interesting graphic about milk. I have one quibble. The problem with hormone exposure from drinking cow's milk comes from the cow's own steroid hormones, mainly estrogen, and from the amount and amino acid balance of the protein in the cow's milk. Thus, it's a problem even with "organic" milk.
Dairy products area major dietary source of estrogen, which can be absorbed from your food. That's why birth control hormones can be given in a pill. As an anabolic hormone, estrogen promotes growth, including the growth of cancers.
The bovine growth hormone that is given to cows is a peptide hormone. It's a small protein, like insulin. Even if a protein hormone were to get into the milk, it would be broken down in the digestive system before it could reach its target tissues. That's why diabetics can't take insulin by mouth.
Although you can't get a peptide hormone directly from the milk, the large load of "high-quality" protein in dairy products provokes your liver to secrete your own insulin-like growth factor (IGF-1), which is identical to the hormone that a cow secretes when exposed to recombinant bovine growth hormone. The problem is the amount and amino acid balance of the protein. You could get a similar effect from eating way too much soy protein. So too much "high-quality" protein in your food, not the BST given to cows, causes the abnormally high levels of IGF-1 in the human body. You are supposed to have some IGF-1 in your system, but having too much promotes cancer and accelerates aging. I think that the fat and estrogen in the dairy products and the IGF-1 that they provoke are likely responsible for the link between lactose consumption and ovarian cancer. I doubt that the lactose, per se, has such an effect.
Many people have voiced concerns about the possible effects of bovine growth hormone on the health of the cows. These effects could be bad for the cows as well as bad for humans who drinke cow's milk. Use of bovine growth hormone could increase the cows' risk of mastitis, or udder infection, which is then treated with antibiotics. That poses problems related to the overuse of antibiotics, which could increase antibiotic resistance in bacteria, as well as increasing the risk of antibiotic residues in the food supply.