When I was in elementary school it seemed like we took a field trip to a dairy farm two or three times a year every year. Not some traditional dairy farm for tourists, but a big factory-style dairy farm owned by a big company that had farms and distribution covering the entire state. They showed us the calves in veal crates.
I don't think it turned many people off milk and cheese. Actually the grossest field trip we ever went on was to a potato chip factory, the stink of rotten potatoes was overwhelming. They never took us to a pig or chicken farm though, I've been to a few at other times and those would have beat the chip factory easily. A lot of people who grow up around cows say they appreciate the small (I do, to an extent) but I've never heard anybody say that about pigs or chickens.