If a person can alter its body composition to become an entirely different species, I don't think it would be a stretch to say that it can choose to become a member of that species that's able to produce milk.

For the same reason, in my world druids can choose the gender of the animal they become. You're a person and you're turning into a bear, and you can already choose to become a black, brown or white bear; there's no reason you couldn't choose if that bear has a dick or not, and I honestly don't care either way.

That being said, I was being sarcastic. Although it's not specified RAW, RAI, it would work just like any other magical transformation: anything that detaches from, is produced by or is separated from the "main" magical body, disappears after a short while. Iirc somewhere on Twitter or the Sage Advice there's confirmation of this (the context wasn't milk produced by a cow-shaped druid, of course, but venom extracted by a viper-shaped druid).

And if a druid asked to feed their party this way, or a party member asked the druid to do this (either with or without their consent) I wouldn't allow it because that's not something I (and probably someone else, too) would be comfortable with.