That opens up the possibility of vegan cheese, butter, etc. but as true dairy products.
There actually are vegan dairy-ish products out there. Several startups have inserted the gene for casein (the main protein in milk) into yeast. So you just harvest the casein, add a little bit of some sort of fat and sugar and you have something that's 99% the same as milk, and can be used in the same sorts of processes.
The only product that I've actually tried was some Brave Robot ice cream, which was well... ice cream.