Ooops, sort of didn't see the mammal part, sorry about that! I shouldn't post while drinking.
Most of the dairy I consume is organic -- all the butter, cream and milk (and recently I found organic buttermilk, yay! great for pancakes and waffles

) and most of the cheese. I f I can't find an organic version of a cheese I want, I try to get a raw milk cheese from another country (usually Europe), or I go for artisan (local, small batch handmade) cheeses. These tend to use better milk in their production.
I will tell you one thing, organic dairy is NOT cheap, being about 3-5x more expensive than non-organic depending on the product.
I def agree with genetics being part of it (as I implied earlier), and a large part of that can be determined by looking at your heritage. I am descended from people who have been consuming lots of dairy for millenia -- at least on my mother's side of the family -- so it makes sense that I should be able to eat it without problems.
I too would prefer to have my own cow (and actually I used to long for a farm overall, and my own eggs etc), or even to just be able to get it from someone whom I know who has cows. Fresh from the cow, unhomogenized/unpasteurized milk has some risks but alot of potential benefits (enzyme and nutrients) and it tastes DELICIOUS!