As an American you have a right to own a goat - or sheep or cow - as long as you keep it in good health and in a facility zoned for such an animal. But in California recent regulatory actions seek to prohibit you from that right. For some reason the CDFA is acting as though it was illegal to own a goat and pay some one else to milk it for you. Neither of these activities are illegal under California or Federal law.
At issue are the private contracts between groups of people called "herd shares". In these contracts a group of people buy a herd of dairy animals and pay a farmer to milk them. They then share in the dairy products produced by their animals. These are not simple contracts and the people who enter into them know the implications and long-term commitments they are making. They are not guaranteed specific production - what they get is dependent on what their animals produce based on feed, time of year, and health of the animals. The only difference between this arrangement and owning one animal youself is that the group of investors is paying someone to board and milk the animals.
Boarding animals is not illegal - you can board dogs, cats, and horses rather readily in any city. Is it so strange that someone might board a goat or cow?
Paying someone to milk your animal is not illegal. I would venture to guess that EVERY large dairy has at least one employee that helps with milking. This is exactly the same type of relationship herd share owners have and its not illegal.
The CDFA says that participating in a herdshare is just a way of getting around dairy laws. But having your own animals and getting their milk for your own purpose is very different than providing milk into the commercial milk supply chain. If you were to accept the CDFA argument it would mean you could not milk your own goat without a Class A dairy license.
Read more about the issues being faced in California at: http://hartkeisonline.com/food-politics/mark-mcafee-writes-letter-of-support-for-california-herdshare-programs/ and