I am not sure about the meaning of "take an interest" here:
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The main concern is the financial interest that the American government has taken in the dairy industry, promoting milk as the best source of calcium.
"Interest" could mean either wanting to be involved in something, or ownership of a share of some business.
So, does the example mean 1) the government is concerned with the finances of the milk industry, or 2) that the government own a portion of the industry?
It means that the government is financially involved with the milk industry, rather than the milk industry being independent of any government influence.
This involvement includes government paid advertising campaigns, and government created markets like the school lunch program.
I believe the government also subsidizes milk production itself, but I don't know specifically.
Approximately your choice #2, except that there is a second, broader and looser sense of interest than strict ownership. A party can also be said to have a financial interest in something if they will be financially impacted by how it turns out. I assure you: I have a financial interest in the fate of the apartment I rent, even if I don't own it. Likewise, while I am in no way an owner of the business I work for, I have a financial interest in its accounts payable procedures.
In this paragraph, the author is not contending that the US government has gotten into the dairy business, but rather the US government has gotten financially involved in some less specific way in the dairy industry.
